if a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the rate of the river and the rate of the boat in still water respectively are

Question

a. 7 & 16 mph
b. 7 & 17 mph
c. 6 & 17 mph
d. 6 & 18 mph
e. none

Answer 1

The easiest way to solve this problem is to break it up into steps.

 

1. First you calculate the speed downstream by dividing the 72 miles traveled by the 3 hours it took. This comes out to a speed of 24 miles/hour downstream.

2. Next you do a similar thing for the speed upstream; 60 miles divided by 6 hours becomes 10 miles/hour.

3. This means that the boats speed plus the current is 24 miles/hour where as the boat's speed minus the speed of the current is 10 miles/hour.

4. Thus the speed of the current is half of the difference between the upstream and downstream speeds. (24 - 10) / 2 = 6 miles/hour.

5. If the speed is 24 miles per hour downstream and we subtract the speed of the current from that we get the speed of the boat in still water. 24 - 6 = 18 miles/hour

 

Therefore, the answer is D; the current has a rate of 6 miles per hour and in still water the boat moves at a speed of 18 miles per hour.

 

Let me know if there is anything still unclear about this problem. I would be happy to explain it.