Question

prabhat cycled a distance of 240 kilometre at a certain speed. if he cycled 3km faster every hour,he would have taken 4 hours fewer to reach the distance. what was the speed in km/h at which prabhat acrually cycled?

Answer 1

Define x:

Let the speed be x km/h

If he cycled 3km faster every hour, the speed will be (x + 3) km/h

Find the time needed when the speed is x km/h:

Distance = 240 km

Speed = x km/h

Time = Distance ÷ Speed

Time = 240/x hour

Find the time needed when the speed is (x + 3) km/h:

Distance = 240 km

Speed = (x + 3) km/h

Time = Distance ÷ Speed

Time = 240/(x + 3) hour

Solve x:

The difference in time taken is 4 hours

240/x - 240/(x + 3) = 4

240(x + 3) - 240x = 4x(x + 3)

240x + 720 - 240x = 4x² + 12x

4x² + 12x - 720 = 0

x² + 3x - 180 = 0

(x - 12)(x + 15) = 0

x = 12 or x = -15 (rejected, since speed cannot be negative)

Find speed:

Speed = x = 12 km/h

Answer: Prabhat is cycling at 12 km/h

Answer 2

solution :-

Let the original speed of Prasoon be s
and original time Prasoon took be t

So,

we have distance = speed x time
180 = st.....(1)

Now, if he cycled 2 km slower his new speed will be = s - 2

new time taken will be = t + 3

So, we have 180 = (s - 2)(t + 3)

180 = st + 3s - 2t - 6......(2)

Solving (1) and (2) we get

180/s = t, from (1) putting this in (2) we get

180 = s(180/s) + 3s - 2(180/s) - 6

180 = 180 + 3s - 360/s - 6

3s - 360/s - 6 = 0

s - 120/s - 2 = 0

s² - 2s - 120 = 0

s² - 12s + 10s - 120 = 0

s(s - 12) + 10(s - 12) = 0

(s - 12)(s + 10) = 0

s = 12 or -10
but speed cant be negative, so s = 12

Therefore, the speed at which Prasoon actually cycled = 12 km/hr