Two persons M and N are to meet at a place 24 km from their place of residence, M owns a scooter which will give him an average 12 kmph more than N and so he agrees to give N a start of 2 hours and arrives at the destination 12 minutes after N. How fast does each travel?
Answers
Given : Two persons M and N are to meet at a place 24 km from their place of residence, M owns a scooter which will give him an average 12 kmph more than N and so he agrees to give N a start of 2 hours and arrives at the destination 12 minutes after N
To find : speeds of M and N.
solution : Let speed of N = x km/h
then speed of M = (x + 12) km/h
N starts first and travel 2 hours after that M starts to move along their destination.
after two hour, remaining distance for N = 24 - 2x
so, time taken by M - time taken by N = 12 minutes
⇒24/(x + 12) - (24 - 2x)/x = 12/60
⇒24/(x + 12) - 24/x + 2 = 1/5
⇒24[x - x - 12]/(x² + 12x) + 2 = 1/5
⇒-288/(x² + 12x) = -9/5
⇒32 × 5 = x² + 12x
⇒x² + 12x - 160 = 0
⇒x² + 20x - 8x - 160 = 0
⇒(x + 20)(x - 8) = 0
⇒x = 8 , -20
but value of x can't be negative.
so, x = 8
Therefore the speed of M = 8 km/h and speed of N = 20 km/h
Answer : The speed of M is 20 km/h and speed of N is 8 km/h
Explanation :
Given : Two persons M and N have to meet at a place 24 km from their place of residence, M owns a scooter which will give him an average 12 km per hour more than N and so he agrees to give N a start of 2 hours and arrives at the destination 12 minutes after N
We need to find : Speed of M and Speed of N.
Solution :
Let speed of N = x km/h
then speed of M = (x + 12) km/h
N starts first and travels 2 hours, after that M starts to move
After 2 hours, remaining distance for N = 24 - 2x
So, time taken by M - time taken by N = 12 minutes
⇒24/(x + 12) - (24 - 2x)/x = 12/60
⇒24/(x + 12) - 24/x + 2 = 1/5
⇒24[x - x - 12]/(x² + 12x) + 2 = 1/5
⇒-288/(x² + 12x) = -9/5
⇒32 × 5 = x² + 12x
⇒x² + 12x - 160 = 0
⇒x² + 20x - 8x - 160 = 0
⇒(x + 20)(x - 8) = 0
⇒x = 8 , -20
But value of x can't be negative.
Therefore, value of x = 8
Thus, the speed of N is 8 km/h
Substituting the value of x, the speed of M is x + 12 = 20 km/h