What is the distance the boat travels each way?

Question

A boat travels 3 hours downstream at r miles per hour. On the return trip, the boat travels 5 miles per hour slower and takes 4 hours.

Answer 1

distance = speed * time

 

The boat travels the same distance downstream as upstream.  Hence:

 

(r mph)*(3 hours) = (r-5 mph)*(4 hours)

 

3r = 4r - 20

20 mph = r

 

Distance = (r mph)*(3 hours) = (20 mph)*(3 hours) = 60 miles

Answer 2

Sometimes there is no obvious formula to use. Instead, try drawing a picture, writing down what you know, and taking a guess.

 

A boat travels 3 hours downstream, but we don't know how fast or how long.

 

The boat travels 4 hours upstream, and went 5 miles per hour (mph) slower than it did going downstream.

 

Let's take a guess:

1) I think it is possible for the boat to travel 10 mph downstream for 3 hours. This assumption tells us it must have traveled 30 miles.

 

2) Now we need to check our guess by using the same speed for downstream: 10 mph - 5 mph (since it went slower) = 5 mph for 4 hours. If the boat travels 5 mph for 4 hours, then it traveled 20 miles.

 

3) Because 30 miles downstream ≠ 20 miles upstream, we know we did not guess correctly.

 

4) Try again.

 

Second Guess:

1)I think it is possible for the boat to travel 20 mph downstream for 3 hours. This assumption tells us it must have traveled 60 miles.

 

2) Now we need to check our guess by using the same speed for downstream: 20 mph - 5 mph (since it went slower) = 15 mph for 4 hours. If the boat travels 15 mph for 4 hours, then it traveled 60 miles.

 

3) 60 miles downstream = 60 miles upstream → The boat travels 60 miles each way.