I don't understand. Please help.

Question

After a sailboat had been on the water for 3 h, a change in the wind direction reduced the average speed of the boat by 2 mph. The entire distance sailed was 91 mi. The total time spent sailing was 5 h. How far did the sailboat travel in the first 3 h?

Answer 1

x = speed on 1st part of the trip, for 3 hrs. x - 2 = speed on 2nd part. Since entire trip is 5 hrs, 2nd part must have been 5 - 3 = 2 hrs.

Total distance = 91 mi.; dist = rate x time

Equation for distance 91 = 3x + 2(x - 2) -> 91 = 3x + 2x - 4. -> 91 = 5x - 4

Add 4 to both sides; 95 = 5x -> divide by 5's -> x = 19 mph

So distance traveled in 1st part is 19 x 3 = 57 mi.

Check: 57 mi in 1st part; 2nd part is 2 hrs x (19 - 2) mph = 2 x 17 = 34 mi. Total 57 + 34 = 91 mi.

Note: I think speed on the water in a sailboat would be specified in knots (?), but that would create a different kind of problem!

Answer 2

They traveled 91 miles in 5 hours, so the overall average speed = 91/5 = 18.2 mph

Let the original speed = s

They traveled at a speed of s for 3 hours, so (s + s + s) ÷ 3 would give us the overall average speed for the first 3 hours traveled.

If s is the speed for the first three hours and the the had decreased by 2 mph for the last 2 hours, then the speed for each of the last 2 hours can be represented by (s - 2).



The last 2 hours, their speed was decreased by 2 mph, so [s + s + s + (s - 2) + (s - 2)] ÷ 5 = 18.2

(5s - 4) ÷ 5 = 18.2

5s - 4 = 91

5s = 95

s = 19 mph

Distance traveled in first 3 hours = 3(19) = 57 miles