- Candle A burns for 8 minutes and is 1.5 cm longer than Candle B - Candle B burns for 5 minutes - They were lit at different times but burned down to the same length at 0705 - Using the concept that if two objects travel the same distance, their speed ratio reverses their time ratio, we can determine that Candle A is 24 cm long.

1. Common Distance
Two candles have different length and thickness.
Candle A is 1.5 cm longer than Candle B.
Candle A can burn for 8 minutes while Candle B
for 5 minutes. Candle A is lit at 0700 and Candle B at
0702. Both are the same length at 0705.
How long is Candle A?
© mathsHeuristics

2. Common Distance
If Object A and Object B travel the SAME DISTANCE
2 km
1 km/h A
2 km/h B
Observation:
© mathsHeuristics
Conclusion:

3. Common Distance
If Object A and Object B travel the SAME DISTANCE
2 km
1 km/h A
2 km/h B
Observation:
A B
Speed 1
Time
© mathsHeuristics
Conclusion:

4. Common Distance
If Object A and Object B travel the SAME DISTANCE
2 km
1 km/h A
2 km/h B
Observation:
A B
Speed 1 2
Time
© mathsHeuristics
Conclusion:

5. Common Distance
If Object A and Object B travel the SAME DISTANCE
2 km
1 km/h A Time = 2 1 = 2 hr
2 km/h B
Observation:
A B
Speed 1 2
Time 2
© mathsHeuristics
Conclusion:

6. Common Distance
If Object A and Object B travel the SAME DISTANCE
2 km
1 km/h A Time = 2 1 = 2 hr
2 km/h B Time = 2 2 = 1 hr
Observation:
A B
Speed 1 2
Time 2 1
© mathsHeuristics
Conclusion:

7. Common Distance
If Object A and Object B travel the SAME DISTANCE
2 km
1 km/h A Time = 2 1 = 2 hr
2 km/h B Time = 2 2 = 1 hr
Observation:
A B
Speed 1 2
Time 2 1
© mathsHeuristics
Conclusion: If two objects travel the same distance:
their Speed Ratio will reverse Time Ratio

8. Common Distance
Two candles have different length and thickness.
Candle A is 1.5 cm longer than Candle B.
Candle A can burn for 8 minutes while Candle B
for 5 minutes. Candle A is lit at 0700 and Candle B at
0702. Both are the same length at 0705.
How long is Candle A?
© mathsHeuristics

9. Two candles have different length and thickness.
Candle A is 1.5 cm longer than Candle B.
Candle A can burn for 8 minutes while Candle B
for 5 minutes. Candle A is lit at 0700 and Candle B at
0702. Both are the same length at 0705.
How long is Candle A?
STEP 1 1.5 cm
A B
© mathsHeuristics
Ans: 24 cm

10. Two candles have different length and thickness.
Candle A is 1.5 cm longer than Candle B.
Candle A can burn for 8 minutes while Candle B
for 5 minutes. Candle A is lit at 0700 and Candle B at
0702. Both are the same length at 0705.
How long is Candle A?
1.5 cm
STEP 2
8 min
5 min
A B
© mathsHeuristics

11. Two candles have different length and thickness.
Candle A is 1.5 cm longer than Candle B.
Candle A can burn for 8 minutes while Candle B
for 5 minutes. Candle A is lit at 0700 and Candle B at
0702. Both are the same length at 0705.
How long is Candle A?
0700
1.5 cm
0702
8 min
STEP 3
5 min
A B
© mathsHeuristics

12. Two candles have different length and thickness.
Candle A is 1.5 cm longer than Candle B.
Candle A can burn for 8 minutes while Candle B
for 5 minutes. Candle A is lit at 0700 and Candle B at
0702. Both are the same length at 0705.
How long is Candle A?
0700
1.5 cm
0702
8 min
5 min
0705
STEP 4
A B
© mathsHeuristics

13. Two candles have different length and thickness.
Candle A is 1.5 cm longer than Candle B.
Candle A can burn for 8 minutes while Candle B
for 5 minutes. Candle A is lit at 0700 and Candle B at
0702. Both are the same length at 0705.
How long is Candle A?
0700
1.5 cm
0702
8 min
3 min
5 min
0705
STEP 4
A B
© mathsHeuristics

14. Two candles have different length and thickness.
Candle A is 1.5 cm longer than Candle B.
Candle A can burn for 8 minutes while Candle B
for 5 minutes. Candle A is lit at 0700 and Candle B at
0702. Both are the same length at 0705.
How long is Candle A?
0700
1.5 cm
0702
8 min
3 min
5 min
0705
STEP 4 2 min
A B
© mathsHeuristics

15. Two candles have different length and thickness.
Candle A is 1.5 cm longer than Candle B.
Candle A can burn for 8 minutes while Candle B
for 5 minutes. Candle A is lit at 0700 and Candle B at
0702. Both are the same length at 0705.
How long is Candle A?
0700
1.5 cm
0702
5 min
8 min
3 min
5 min
0705
STEP 4 2 min
A B
© mathsHeuristics

16. Two candles have different length and thickness.
Candle A is 1.5 cm longer than Candle B.
Candle A can burn for 8 minutes while Candle B
for 5 minutes. Candle A is lit at 0700 and Candle B at
0702. Both are the same length at 0705.
How long is Candle A?
0700
1.5 cm
0702
5 min
8 min
3 min
5 min
0705
STEP 4 3 min 2 min
A B
© mathsHeuristics

17. Two candles have different length and thickness.
Candle A is 1.5 cm longer than Candle B.
Candle A can burn for 8 minutes while Candle B
for 5 minutes. Candle A is lit at 0700 and Candle B at
0702. Both are the same length at 0705.
How long is Candle A?
0700
1.5 cm
0702
5 min
8 min
3 min
5 min
0705
3 min Same distance 2 min
A B
STEP 5 Same distance : Speed Ratio will reverse Time Ratio
A B
© mathsHeuristics
Speed
Time 3 2

18. Two candles have different length and thickness.
Candle A is 1.5 cm longer than Candle B.
Candle A can burn for 8 minutes while Candle B
for 5 minutes. Candle A is lit at 0700 and Candle B at
0702. Both are the same length at 0705.
How long is Candle A?
0700
1.5 cm
0702
5 min
8 min
3 min
5 min
0705
3 min Same distance 2 min
A B
STEP 5 Same distance : Speed Ratio will reverse Time Ratio
A B
© mathsHeuristics
Speed 2u 3u
Time 3 2

19. Two candles have different length and thickness.
Candle A is 1.5 cm longer than Candle B.
Candle A can burn for 8 minutes while Candle B
for 5 minutes. Candle A is lit at 0700 and Candle B at
0702. Both are the same length at 0705.
How long is Candle A?
0700
1.5 cm
0702
5 min
16u 8 min
3 min
5 min
0705
3 min 2 min
A B
STEP 5 Same distance : Speed Ratio will reverse Time Ratio
A B Height of Candle A => 2u x 8 = 16u
© mathsHeuristics
Speed 2u 3u
Time 3 2

20. Two candles have different length and thickness.
Candle A is 1.5 cm longer than Candle B.
Candle A can burn for 8 minutes while Candle B
for 5 minutes. Candle A is lit at 0700 and Candle B at
0702. Both are the same length at 0705.
How long is Candle A?
0700
1.5 cm
0702
5 min
16u 8 min
3 min
5 min 15u
0705
3 min 2 min
A B
STEP 5 Same distance : Speed Ratio will reverse Time Ratio
A B Height of Candle A => 2u x 8 = 16u
© mathsHeuristics
Height of Candle B => 3u x 5 = 15u
Speed 2u 3u
Time 3 2

21. Two candles have different length and thickness.
Candle A is 1.5 cm longer than Candle B.
Candle A can burn for 8 minutes while Candle B
for 5 minutes. Candle A is lit at 0700 and Candle B at
0702. Both are the same length at 0705.
How long is Candle A?
0700
1.5 cm 1u
0702
5 min
16u 8 min
3 min
5 min 15u
0705
3 min 2 min
A B
STEP 5 Same distance : Speed Ratio will reverse Time Ratio
A B Height of Candle A => 2u x 8 = 16u
© mathsHeuristics
Height of Candle B => 3u x 5 = 15u
Speed 2u 3u Difference => 16u – 15u = 1u
Time 3 2

22. Two candles have different length and thickness.
Candle A is 1.5 cm longer than Candle B.
Candle A can burn for 8 minutes while Candle B
for 5 minutes. Candle A is lit at 0700 and Candle B at
0702. Both are the same length at 0705.
How long is Candle A?
0700
1.5 cm 1u
0702
5 min
16u 8 min
3 min
5 min 15u
0705
3 min 2 min
A B
STEP 5 Same distance : Speed Ratio will reverse Time Ratio
A B Height of Candle A => 2u x 8 = 16u
© mathsHeuristics
Height of Candle B => 3u x 5 = 15u
Speed 2u 3u Difference => 16u – 15u = 1u
Time 3 2 1u = 1.5 cm

23. Two candles have different length and thickness.
Candle A is 1.5 cm longer than Candle B.
Candle A can burn for 8 minutes while Candle B
for 5 minutes. Candle A is lit at 0700 and Candle B at
0702. Both are the same length at 0705.
How long is Candle A?
0700
1.5 cm 1u
0702
5 min
16u 8 min
3 min
5 min 15u
0705
3 min 2 min
A B
STEP 5 Same distance : Speed Ratio will reverse Time Ratio
A B Height of Candle A => 2u x 8 = 16u
© mathsHeuristics
Height of Candle B => 3u x 5 = 15u
Speed 2u 3u Difference => 16u – 15u = 1u
Time 3 2 1u = 1.5 cm
16u = 16 x 1.5 cm = 24 cm
Ans: 24 cm