Rohit and Rahul start from the same point and move away from each other at right angle. After 4 hours they are 80 km apart. if the speed of Rohit is 4 kmph more than Rahul. what is the speed of Rohit?
Answers
Answer: The speed of Rohit is 16 km/h.
Step-by-step explanation:
Let the speed of Rahul = x km/h,
⇒ The speed of Rohit = (x+4) km/h ( Given )
Now, the distance covered by Rahul in 4 hours = 4x (Distance = speed × time )
While, the distance covered by Rohit in 4 hours = 4(x+4) ,
Since, After 4 hours they are 80 km apart.
Also, they are travelling at right angle,
By the Pythagoras theorem,
(The distance covered by Rahul in 4 hours)² + (The distance covered by Rohit in 4 hours)² = 80²
⇒ 16 x² + 16(x+4)² = 6400
⇒ 16 x² + 16 x² + 256 + 128 x = 6400
⇒ 32 x² + 128 x + 256 - 6400 = 0
⇒ 32 x² + 128 x - 6144 = 0
⇒ x² + 4x - 192 = 0
⇒ x² + 16 x - 12 x - 192 = 0
⇒ x(x+16)-12(x+16) =0 ⇒ (x+16)(x-12) = 0
If x + 16 = 0 ⇒ x = -16 ( Not possible )
If x - 12 = 0 ⇒ x = 12,
Hence, the speed of Rahul = x = 12 km/h,
And, the speed of Rohit = x + 4 = 12 + 4 = 16 km/h
