A car drives downhill with the speed of 90 m/h. On a level road, the same car goes 72 m/h, and uphill it goes "only" 60 m/h.
It takes this car 5 hours to go from town A to town B. The return trip only takes 4 hours.
Find the distance between the two towns.
Let's say from A to B:
x = miles going uphill
y = miles on a level road
z = miles going downhill
Time = Distance / Rate of speed
so...
x/90 + y/72 + z/60 = 5 hours
and
x/60 + y/72 + z/90 = 4 hours
subtract the two equations together and you have:
(x/90 + z/60)  (x/60 + z/90) = 1 hour
using more algebra (is it okay if I leave this as an exercise to the reader?), we can find that
z = 180 + x
and then plugging back into one of the first equations up top:
y = 124  2x
Remember that we want to find the TOTAL distance between A and B, not the individual distances of x, y, and z. So we want to find:
x + y + z
= x + (1242x) + (180+x)
= 304 miles

Posted by Happy
on 20020515 09:14:35 