didtance between a and bis 495 km after traveling a certain distance a motor bike break down and its speed reduce by 37.5% and reaches 90 minute late if bike had brokendown after travelling 45kh more he would have resch18minute aroier find out distance and speed
Answers
Step-by-step explanation:
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}
x
y
+
0.375x
495−y
hours.
So, \frac{y}{x} + \frac{495 - y}{0.375x} = \frac{495}{x} + 1.5
x
y
+
0.375x
495−y
=
x
495
+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
x
y+45
+
0.375x
495−45−y
=
x
495
+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
x
y+45
+
0.375x
450−y
=
x
495
+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)
Answer:
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