Question

By driving 8 mph faster than Bob, John can make a 230 mile trip in one half hour less.How fast does Bob drive on the trip? Round your answer to the nearest mile per hour

Answer 1

57 mph

Explanation:

Let b represent Bob's speed on the trip. Then his time is ...

time = distance/speed

Bob's time = 230/b

Then John's speed is b+8, and his time is ...

John's time = 230/(b+8)

The difference of their times is 1/2 hour:

Bob's time - John's time = 1/2

230/b -230/(b+8) = 1/2 . . . substitute the expressions for time

460(b+8 -b) = b(b+8) . . . . . multiply by 2b(b+8)

b^2 +8b -3680 = 0 . . . . . . .put in standard form

(b +4)^2 -3696 = 0 . . . . . . . add 16-16 to complete the square

b = -4 +√3696 ≈ 56.795 . . . solve for positive b

Bob's drove about 57 mph on the trip.