Question

(The distance from town
A to town B is 180 km. If a cyclist rides
half the distance from A to B with a
specific speed and the other half
distance at a speed 15 km/h more
than the first half. He travelled for 5
hours. Find his speed for the first half)​

Answer 1

Step-by-step explanation:

Distance between town A & B is 180 km

Let

The cyclist covered first half of the distance at the speed of x km/hr

So

his speed for the next half distance = (x+15) km/hr

Now

Distance for the both the halves = 180/2 = 90 km

&

Speed for first half = x km/hr

Speed for second half = (x+15) km/hr

Also

Time = distance / speed

& given that total time taken by him = 5 hrs

Total time taken =

time taken in first half + time taken in second half

=> 90/x + 90/(x+15) = 5

= {(90x + 1350) + 90x}/x(x+15) = 5

= 90x + 1350 + 90x = 5(x^2 + 15x)

= 180x + 1350 = 5x^2 + 75x

= 5x^2 + 75x - 180x - 1350 = 0

= 5x^2 - 105x - 1350 = 0

= x^2 - 21x - 270 = 0

= x^2 - 30x + 9x - 270 = 0

= x(x - 30) + 9(x - 30) = 0

= (x - 30) (x + 9) = 0

= (x - 30) = 0 & (x + 9) = 0

=> x = 30 & - 9

But speed cannot be negative so

X = 30

So speed in his first half = 30 km/hr