SOLUTION: Bob made a trip of 282 miles.He averaged 63 mph for the first part and 52 mph for the second part.If the trip took 5 hours, how long did he travel at each rate?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Bob made a trip of 282 miles.He averaged 63 mph for the first part and 52 mph for the second part.If the trip took 5 hours, how long did he travel at each rate?      Log On


   

Question 1071115: Bob made a trip of 282 miles.He averaged 63 mph for the first part and 52 mph for the second part.If the trip took 5 hours, how long did he travel at each rate?
Answer by ikleyn(52858) About Me  (Show Source):
You can put this solution on YOUR website!
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Bob made a trip of 282 miles.He averaged 63 mph for the first part and 52 mph for the second part.
If the trip took 5 hours, how long did he travel at each rate?
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Solution 1 (Two equations) 

Let x be the time traveled at average speed of 63 mph, 
and y be the time traveled at 52 mph.

Then you have these two equations for the two unknowns

  x +   y =   5,         (1)     ("the trip took 5 hours")
63x + 52y = 282.         (2)     (the entire traveled distance).

Set up is completed. The rest is on you.

Solution 2 (One equation) 

Let x be the time traveled at average speed of 63 mph, in hours. 
Then the time traveled at 52 mph is 5-x hours.

Then you have this "distance equation"

63x + 52*(5-x) = 282. 

Simplify and solve it for x.