A car moves at a steady pace from point P to point Q. It would have taken an hour less if it had accelerated by 10 km/h. It would have saved an additional forty-five minutes if its speed had been increased by an additional ten kilometers per hour. How far are P and Q apart?
Show answer & explanation
Correct answer: A
Explanation
Given:
Increase in speed by 10 km/h → time reduced by 1 hour
Increase in speed by 20 km/h → time reduced by 1 hour 45 minutes
Formula:
Distance = Speed × Time
Let original speed = x km/h
Time = t hours
Distance = xt
First case:
xt = (x + 10)(t − 1)
xt = xt + 10t − x − 10
10t − x − 10 = 0
x = 10t − 10 ……(1)
Second case:
1 hour 45 minutes = 7/4 hours
xt = (x + 20)(t − 7/4)
xt = xt + 20t − 7x/4 − 35
20t − 7x/4 − 35 = 0
80t − 7x − 140 = 0 ......(2)
Now from (1)
x = 10t − 10
Substitute this into (2):
80t − 7(10t − 10) − 140 = 0
80t − 70t + 70 − 140 = 0
10t − 70 = 0
t = 7
x = 10(7) − 10
x = 60 Distance
= xt = 60 × 7 = 420 km