Problema Solution
1. The motorboat could go 15 miles downstream in 3 hours, but took 2 hours longer to go 10 miles upstream. What is the speed of the current?
2. If a boat in a 4 MPH current can travel 76 miles downstream in the same time it takes to travel 20 miles upstream, what is the speed of the boat in still water?
Answer provided by our tutors
1. Let speed of current be x and speed of boat be y miles/hour.
Effective downstream velocity = y + x ; time = 3 hours; distance 15 miles
Effective upstream velocity = y - x ; time = 3+2 hours (since it took 2 hours more); distance 10 miles
Time = Distance / Speed
3 = 15 / (y + x) --> y + x = 5 ... (a)
5 = 10 / (y - x) --> y - x = 2 .... (b)
Solving (a) and (b), x = 1.5 miles/hour
2. Let speed of boat be x mph.
Downstream: speed = x + 4 mph, distance = 76 miles
Upstream: speed = x - 4 mph, distance = 20 miles
Since time taken is the same, and using the relation time = distance/speed
76 / (x+4) = 20 / (x-4) --> x = 6.86 mph