Jim takes a seconds to swim c 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 b 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?
We are given jim's rate and rogers rate in addition to the size of the pool. Also, we know that Roger is faster than Jim.
The portion in blue implies that Roger can swim the same distance in less time. However, when Jim and Roger cross paths in the pool, the time they will have traveled will be the same. Because the time that they spend swimming is the same we can say time = t.
If t is the same for both swimmers than why can't we just multiply their respective rates by t? Why do we have to solve out for t?
We know the rate of both swimmers. We also know that the time they spend swimming is the same. We also know the length of the pool. We can do a combined distance formula where:
(rate Jim)*(t) + (rate Roger)*(t) = c
(c/a)*t + (c/b)*t = c
ct/a + at/b = c
We are given jim's rate and rogers rate in addition to the size of the pool. Also, we know that Roger is faster than Jim.
The portion in blue implies that Roger can swim the same distance in less time. However, when Jim and Roger cross paths in the pool, the time they will have traveled will be the same. Because the time that they spend swimming is the same we can say time = t.
If t is the same for both swimmers than why can't we just multiply their respective rates by t? Why do we have to solve out for t?
We know the rate of both swimmers. We also know that the time they spend swimming is the same. We also know the length of the pool. We can do a combined distance formula where:
(rate Jim)*(t) + (rate Roger)*(t) = c
(c/a)*t + (c/b)*t = c
ct/a + at/b = c