Jim takes a seconds to swim u meters at a constant rate from point P to point Q in a pool. Roger, who is faster than Jim, can swim the same distance in v seconds at a constant rate. If Jim leaves point P the same time that Roger leaves point Q, how many fewer meters will Jim have swum than Roger when the two swimmers pass each other?
Choose the most appropriate option:
A) c(v-u)/ (v+U)  B) c(a-b)/a+b  C) c(a+b)/a-b  D) ab(a-b)/a+b  E) ab(b-a)/a+b
Both JimRoger are travelling at constant speedin opposite direction: and c is the distance   So, speed of Jim = c/u speed of Roger = c/v   Let say Jim travelled distance x from P where it met Roger, it means that Roger travelled (c-x) from point Q   [x would be less than (c-x) as Jim is travelling slow]   From above, time taken by Jim to travel x = xu/c....................... (1)   Also, time taken by Roger to travel (c-x) = (c-x)v/c.....................(2)   Time taken by both JimRoger is same, so (1) = (2)   xu/c = (c-x)v/c,   Solving further, x = vc/(u+v).................... (3)   We require to find how many fewer meters will Jim have swum i.e   additional distance travelled by Roger = (c - x) - x   = c-2x   Substituting value of x from (3)solving the equation further, we get c(v-u)/ (v+U)nswer = c(v-u)/v+u   c(v-u)/ (v+U)nswer = (c(v-u)/ (v+U))
<result>A</result>
Jim takes a seconds to swim u meters at a constant rate from point P to point Q in a pool. Roger, who is faster than Jim, can swim the same distance in v seconds at a constant rate. If Jim leaves point P the same time that Roger leaves point Q, how many fewer meters will Jim have swum than Roger when the two swimmers pass each other?