The cruise ship traveled n miles per hour for t hours and was 30 miles short of the harbor when the horn was sounded.

Question

If the captain tried again, how long would it take to reach the harbor if she increased the rate of travel by 15 mph?

Answer 1

Distance = rate * time

D = r*t + 30 = (r+15)*t

So r*t + 30 = r*t + 15t

Or 15t = 30

t = 2 hours

Answer 2

Hi there,

Distance= rate*time

So from the first portion of the problem,

D₁=nt

Let D₂ be the remainder of the trip, 30.

Hence, the total distance from start to the harbor would be

nt+30.

If the ship were to increase the speed by 15 mph, the distance traveled would be

(n+15)x,

where x is the time that it takes to get to the harbor from the start. Note the problem didn’t specify whether or not it took the same time, t, to get there when the speed increased 15 mph. Therefore, we should use another variable.

Now, simply equate (n+15)x= nt+30 since distance is conserved.

Solve for x:

x=(nt+30)/(n+15) hours

I hope this helps!