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Question

A. A boat traveled downstream a distance of 80 mi and then came right back. If the speed of the current was 20 mph and the total trip took 5 hours and 20 minutes, find the average speed of the boat relative to the water.

B. Meg rowed her boat upstream a distance of 7 mi and then rowed back to the starting point. The total time of the trip was 8 hours. If the rate of the current was 3 ​mph, find the average speed of the boat relative to the water.

Answer 1

160/(5 1/3) =30 mph

interestingly the speed of the boat in still water is 40 mph, not 30 mph

40mph +20mph = 60 mph downstream for 1 hour and 20 minutes = 80 miles

40mph-20mph = 20mph upstream for 4 hours = 80 miles

so the question may be ambiguous. average speed of the boat relative to still water is 40 mph

but the average speed of the boat in the water = 30 mph

same situation with the 2nd problem

14/8 =1.75 mph = average speed in the water over 8 hours

but 1.75 mph is not the average speed of the boat relative to still water

speed of the boat in still water = 4 mph

downstream: 4+3 = 7 mph covering 7 miles in 1 hour

upstream 4-3 = 1 mph covering 7 miles in 7 hours

for a total 14 miles in 8 hours

since the problems gives the current speed as if it were needed to find the solution

odds are the answers you want are 40 mph and 4 mph

not 30 mph and 1.75 mph

d/t=s

distance divided by time = speed