find the speed of the rickshaw and the bus
Answers
Answer
Speed of rickshaw and bus is 10km/hr and 40km/hr respectively.
Solution
Let the speed of rickshaw and bus x km/hr and y km/hr respectively.
Now time taken to travel by rickshaw is 2 hr so,
t1 = 2/ x hr
Because speed= distance/ time .So , time = distance/ speed .
Distance travelled by bus is (14-2)= 12km. So, time will be
t2 = 12/y hr
Total time taken to travel this distance is
t1 + t2 = 1/2 = 2/x + 12/y .......(1)
Now according to other condition
Time taken to travel by rickshaw is
t3 = 4/x
Time taken to travel by bus is
t4 = 10/y . Total time taken to travel this distance is
t3 + t4 = 1/2+9/60 = 4/x + 10/y
4/x + 10/y =13/20 ............(2)
Let 1/ x = u and 1/y = v .
Then eq 1 and 2 will be
eq 1st = 2×1/x + 12× 1/y
= 2u + 12v ............(3)
eq 2nd = 4×1/x + 10×1/y
= 4u +10v .......(4)
Now multiple eq3 by 2 and Substracting by 4th
= (4u +24v )- (4u +10v) = 1-13/20
= 14v = 7/20
= v. = 1/40
Putting the value of v in equation 3
= 2u + 12(1/40) = 1/2
= 2u = 2/10
= u. = 1/10
So , required values are:
x = 1/u = 10km/hr
y = 1/v = 40km/hr .