Question

Mr. and Mrs. Das were travelling by car from Delhi to Kasauli for a holiday. Distance between Delhi and Kasauli is approximately 350 km (via NH 152D). Due to heavy rain they had to slow down. The average speed of the car was reduced by 20 km/hr and time of the journey increased by 2 hours. Find:

1. the original speed of the car. 
2. with the reduced speed, the number of hours they took to reach their destination.

Answer 1

(a) Let the original speed of the car be x km/hr. Distance between Delhi and Kasauli = 350 km

`Time = "Distance"/"speed" = 350/x`

Due to heavy rain, the speed is reduced by 20km/hr. So, the new speed is (x − 20) km/hr.

New time = `350/(x − 20) hours`

According to the question,

`350/(x − 20) = 350/x + 2`

`350/"x − 20" − 350/x + 2`

`((350 − 350)(x − 20))/((x − 20)x) = 2`

`(350x − 350x + 7000)/(x2 − 20x) = 2`

2x2 − 40x = 7000

2x² − 40x − 7000 = 0

x² − 20x − 3500 = 0

x² − 70x + 50x – 3500 = 0

x(x − 70) + 50(x – 70) = 0

(x + 50)(x − 70) = 0

x = 70 `(km)/(hr)`

Since speed cannot be negative, the original speed is 70 km/hr.

(b) With the reducece speed, the number of hours they took to reach their destination is: 

Time = `350/(70 − 20)`

= `350/50`

7 hours