The rowing team was initially rowing upstream at 1.5 mph against a 15 mph downstream current. After 12 minutes, a hat was dropped and floated downstream. It took the team 15 more minutes to notice. They then turned around and began rowing downstream at a combined speed of 31.5 mph (boat speed + current). To catch the hat, they had to make up a distance of 16.5/4 km in that time. Given their relative speed to the hat was now 16.5 mph, it would take them 15 minutes to catch up.

1. Speed, Time and Distance

2. Speed, Time and Distance
A river is flowing downstream at 15 mph relative to the shore. A rowing team is
practicing rowing and at first they row upstream (against the current) and can only go
1.5 mph relative to the shore. The man at the back of the boat is wearing a hat when
they begin, but after 12 minutes his hat falls into the water (and floats) and it is 15
minutes since it has fallen before they notice it. They then, instantaneously reverse
direction and row back to catch up with the hat, rowing with the same strength and
power with which they were rowing before. How long will it take them to catch up
with the hat?
(a) 16.5 min (b) 15 min
(c) 15.25 min (d) 31.5 min

3. Speed, Time and Distance
Upstream speed of boat = 1.5 mph; Speed of stream = 15 mph
Still water speed of boat = 16.5 mph
A river is flowing downstream at 15 mph relative to the shore. A rowing team is
practicing rowing and at first they row upstream (against the current) and can only go
1.5 mph relative to the shore. The man at the back of the boat is wearing a hat when
they begin, but after 12 minutes his hat falls into the water (and floats) and it is 15
minutes since it has fallen before they notice it. They then, instantaneously reverse
direction and row back to catch up with the hat, rowing with the same strength and
power with which they were rowing before. How long will it take them to catch up
with the hat?

4. Speed, Time and Distance
Therefore, downstream speed of boat = 16.5 + 15 = 31.5
They notice that the hat has fallen 15 minutes after it had fallen. During this 15 min
the hat would have moved downstream with the river at the speed of the stream.
∴ The distance between the hat and the boat when they notice it = time × relative
speed between boat and hat
15
60
× (1.5+15)=
16.5
4
km
When the boat was turned around to catch up with the hat, the relative distance it
has to cover =
16.5
4
km

5. Speed, Time and Distance
Time taken to cover this distance =
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑆𝑝𝑒𝑒𝑑
Relative speed = (Downstream speed of boat) – Speed of hat = 31.5 – 15 = 16.5 km/hr.
Time taken to catch up =
16.5
4
16.5
= 1/4 hour = 15 minutes
Answer Choice (b)

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