Question

Distance between A and B is 495 km. After travelling a certain distance, a motorbike breaks down and then its speed reduced by 37.5% and reaches 90 minutes late. If the bike had broken down after travelling a distance at 45 km more. He would have reached 18 min earlier. Find out speed of bike and distance of accident place from starting

Answer 1

The speed of the bike is 250 km per hour and the distance of accident place from starting is 270 km.

Step-by-step explanation:

Let the speed of the bike is x km per hour and the distance of accident place from starting is y km.

Now, the distance between A and B is 495 km and after travelling a certain distance, a motorbike breaks down and then its speed reduced by 37.5% and reaches 90 minutes late.

Then, the time taken by the biker to reach his destination is $\frac{y}{x} + \frac{495 - y}{0.375x}$ hours.

So, $\frac{y}{x} + \frac{495 - y}{0.375x} = \frac{495}{x} + 1.5$ {Since, 90 minutes = 1.5 hours}

⇒ 0.375y + 495 - y = 0.375 × 495 + 1.5 × 0.375x

⇒ 0.5625x + 0.625y = 309.375 ......... (1)

Now, if the bike had broken down after travelling a distance at 45 km more. He would have reached 18 min earlier.

So, $\frac{y + 45}{x} + \frac{495 - 45 - y}{0.375x} = \frac{495}{x} + 1.5 - 0.3$ {Since 18 minutes is 0.3 hours}

⇒ $\frac{y + 45}{x} + \frac{450 - y}{0.375x} = \frac{495}{x} + 1.2$

⇒ 0.375(y + 45) + (450 - y) = (0.375 × 495) + (1.2 × 0.375x)

⇒ 0.45x + 0.625y = 281.25 ......... (2)

Now, solving equations (1) and (2) we get,

0.1125x = 28.125

⇒ x = 250 km/hr.

And from equation (2) we get,

0.625y = 168.75

⇒ y = 270 km

So, the speed of the bike is 250 km per hour and the distance of accident place from starting is 270 km. (Answer)