.
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?
~~~~~~~~~~~~~~~~~~~~~~~~~~~
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.