Question

Jack travels to work on the eastern freeway. he notices that the difference in time between if he drives 5 mph below the speed limit an if he drives 15 mph below the speed limit is 2 minutes. Given that the distance for which he uses the freeway is 10 miles.. Find the speed limit of the freeway

Answer 1

Remark

Interesting question. He goes 10 miles no matter what his speed. Let the speed limit = x

Givens

d = 10 miles

r - 5 mph = r1

r - 15 mph = r2

t = 2 minutes

t = 2/60 = 1/30 hours

Formula

10/(r - 15) - 10/(r - 5) = 1/30 hours Take out the common factor of 10

Sub and solve

10 (1 / (r - 5) - 1/(r - 15) ) = 1/30 Divide by 10

1/(r - 15) - 1/(r - 5) = 1/300

Put over a common denominator. (r - 5)(r - 15)

`((r - 5) - (r - 15) )/((r - 5)*(r - 15)) = (15- 5)/((r - 5)*(r - 15)) = (10)/((r - 5)*(r - 15)) = (1)/(300)`

Cross multiply

300 * 10 = (r - 5)(r - 15) Remove the brackets.

3000 = r^2 - 20r + 75 Add 3000 to both sides.

r^2 - 20r - 2925 = 0

The monster factors (believe it or not)

(r - 65)(r + 45) = 0

The rate that works is

r - 65 =0

r = 65

The other rate is - 45 and it has no meaning.

Surely your were not expected to do this as I have done it.