SOLUTION: 6. One bus left Denver at 3 pm going west at 40 mph and another left at 5 pm going west at 60 mph. How many hours will it take the second bus to catch up to the first? Round to t

Algebra ->  Equations -> SOLUTION: 6. One bus left Denver at 3 pm going west at 40 mph and another left at 5 pm going west at 60 mph. How many hours will it take the second bus to catch up to the first? Round to t      Log On


   

Question 619795: 6.
One bus left Denver at 3 pm going west at 40 mph and another left at 5 pm going west at 60 mph. How many hours will it take the second bus to catch up to the first? Round to the nearest tenth if necessary.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let t be the time in hours the second bus is on the road.
Then
Since the distance is the same for both, you can equate
Distance1+=+Distance2
Speed1+%2A+Time1+=+Speed2+%2A+Time2
40+%2A+%28t%2B2%29+=+60+%2A+t
40t+%2B+80+=+60t
80+=+20t
4+=+t
So the second bus will catch up in 4 hours.
Another way to think thru this problem is to realize the first bus had a 2 hour head start. At 40 mph, the first bus is 80 miles ahead of the second bus.
The two buses are traveling at a difference in speed of 20mph.
How many hours will it take to catchup 80 miles at 20mph? Again the answer is 4 hours.
Always more than one way to look at a math problem. :)