Ram & Shyam run a race of 2000 meter. First, Ram gives Shyam a start of 200m and beats him by 30 sec. Next, Ram gives Shyam a start of 3 min and is beaten by 1000 meters. Find the time in minutes in which Ram and Shyam can run the race separately?
(a) 8,10
(b) 4,5
(c) 5,9
(d) 6,9
(e) 9,12
b) 4,5 min
Here is the solution
Let their speeds be R and S resp
Now equating a specified amount of time(Distance/speed), the equations are
(2000/R)=(1800-30S)/S
and
(1000/R)=(2000-180S)/S
These are difficult to solve directly
So substitute 1/R by r and 1/S by s
We get the equations as
2000r=1800s-30
and
1000r=2000s-180
Solving we get r=3/25 and s=3/20 implies
R=25/3 mt/sec and S=20/3 mt/sec
time reqd is 2000*(3/25)*(1/60)=4min and 2000*(3/20)*(1/60)=4min
Please suggest if there is an easy method