Question

A boy can row a boy at a constant speed of 5 mi/ hr in still water. he rows upstream for 20 minutes then rows downstream for 12 minutes returning at his starting point. Find total distance traveled if rate is 1.25 upstream is 5-x downstream is 5+x

Answer 1

row a boat

Answer 2

Let speed of current = c

speed against current (upstream) = 5 - c

speed downstream = 5 + c

distance traveled = speed x time

distance traveled upstream = (1/3)(5 - c) [because 20 min = 1/3 h]

distance traveled downstream = (1/5)(5 + c) [because 12 min = 1/5 h]

but these distances are the same so (1/3)(5 - c) = (1/5)(5 + c)

Multiply both sides by 15 to get rid of the fractions:

5(5 - c) = 3(5 + c)

25 - 5c = 15 + 3c

10 = 8c

c = 1.25 mph → so you're right and just about finished

Total distance = (1/3)(5 - c) + (1/5)(5 + c)

subs for c:

= (1/3)(5 - 1.25) + (1/5)(5 + 1.25)

= 2.5 mi