A bus with 12 soccer players broke down in a town 20 miles f

A bus with 12 soccer players broke down in a town 20 miles from its destination. The coach

Solution

We make this diagram, where the broken-down bus is at A and the destination is at F. B,C,D, and E are points along the way with unknown distances v,w,x,y,z miles between them. | v miles | w miles | x miles | y miles | z miles | ------------------------------------------------------------ A B C D E F We of course have the first equation as v + w + x + y + z = 20 Here are the 5 trips the car makes. 1. Car drives from A to D. (1st 4 get out and walk from D to F.) 2. Car drives from D to B. (picks up 2nd 4, who have walked from A to B.) 3. Car drives from B to E. (2nd 4 get out and walk from E to F.) 4. Car drives from E to C. (picks up 3rd 4, who have walked from A to C.) 5. Car drives from C to F. Now we\'ll fill in the details: 1. Car takes 1st 4 from A to D, a distance of v+w+x miles. When car gets to D, it has traveled v+w+x miles and therefore (v+w+x)/20 hours have passed, using TIME = DISTANCE/RATE. [Then the 1st 4 have y+z miles yet to walk to F, which will take them (y+z)/4 hours. So total time = (v+w+x)/20 + (y+z)/4 hours, or simplifying, total time = (v+w+x+5y+5z)/20 hours.] 2. Car drives from D to B, a distance of x+w miles, which takes (x+w)/20 hours more. When car gets to B, (v+w+x)/20 + (x+w)/20, or (v+2w+2x)/20 hours have passed. During this time the 2nd and 3rd 4 have walked from A to B and using Distance=Rate