A man sets out to cycle from delhi to rohtak and at the same time another man starts from rohtak to cycle to cycle to delhi. After passing each other they completed their journey in (10/3) hours and (16/3) hours respectively. At what rate does the second man cycle if the first cycle at 8 kmph?
a. 6.12 kmph
b. 6.42 kmph
c. 6.22 kmph
d. 6.32 kmph
Answers
Answer:
c.
Step-by-step explanation:
Answer:
Let the man from Delhi be A and that from rohtak be B.
After passing each other A takes 10/3 hrs to reach Rohtak.
The speed of 8kmph.
The distance from their meeting point to rohtak is :
10/3 × 8 = 80/3 km
Let the total distance be x.
The distance traveled by B to Delhi is :
= (X - 80/3) km
Time = 16/3 hrs
They took the same time to meet A having traveled (x - 80/3)km and B having traveled 80/3 km
Let speed of B be y
(X - 80/3)/8 = (80/3) / y
Xy - 80/3y = 640/3
y (x - 80/3) = 640/3
Y = (640/3) / (x - 80/3)
The second face of the journey :
A takes = (80/3) /8 hrs
B takes = (x - 80/3) / y = 16/3
= 3x - 80 = 16y
Substituting the value of y in this we have :
3x - 80 = 16{(640/3)/(x - 80/3)
(3x - 80)(x - 80/3) = 10240/3
3x² - 80x - 80x + 6400/3 = 10240/3
3x² - 160x + 6400/3 = 10240/3
3x² - 160x - 3840/3 = 0
3x² - 160x - 1280 = 0
We solve for x using quadratic formula :
{160 +/- √(160² + 4 × 3 × 1280)} /2 × 3
{160 +/- 202.39} /6
x = 60.40 km
Lets substitute this value in the following equation :
3x - 80 = 16y
We have :
3 × 60.4 - 80 = 16y
101.2 = 16y
Y = 101.2/16
= 6.325 km/h
Step-by-step explanation: