SOLUTION: If a scooterist drives at the rate of 24km/hr, he reaches his destination 5 minutes too late. If he drives at the rate of 30km/hr, he reaches his destination 4 minutes too soon.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: If a scooterist drives at the rate of 24km/hr, he reaches his destination 5 minutes too late. If he drives at the rate of 30km/hr, he reaches his destination 4 minutes too soon.       Log On


   

Question 879991: If a scooterist drives at the rate of 24km/hr, he reaches his destination 5 minutes too
late. If he drives at the rate of 30km/hr, he reaches his destination 4 minutes too soon.
How far is his destination ?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the distance he travels
Let +t+ = the " on time " time
----------------------------
(1) +d+=+24%2A%28+t+%2B+5%2F60+%29+
(2) +d+=+30%2A%28+t+-+4%2F60+%29+
-------------------------
By substitution:
+24%2A%28+t+%2B+1%2F12+%29+=+30%2A%28+t+-+1%2F15+%29+
+24t+%2B+24%2F12+=+30t+-+30%2F15+
+6t+=+2+%2B+2+
+t+=+2%2F3+
and
(1) +d+=+24%2A%28+t+%2B+5%2F60+%29+
(1) +d+=+24%2A%28+2%2F3+%2B+5%2F60+%29+
(1) +d+=+24%2A%28+40%2F60+%2B+5%2F60+%29+
(1) +d+=+24%2A%28+45%2F60+%29+
(1) +d+=+24%2A%28+3%2F4+%29+
(1) +d+=+18+
The destination is 18 km away
check:
(1) +d+=+24%2A%28+t+%2B+5%2F60+%29+
(1) +18+=+24%2A%28+40%2F60+%2B+5%2F60+%29+
(1) +18%2F24+=+45%2F60+
(1) +3%2F4+=+3%2F4+
OK
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