SOLUTION: � At first a runner jogs at 5 mph and then jogs at 8 mph traveling 7 miles in 1.1 hours. How long does the runner jog at each speed. (Hint: Let t represent the amount of time the

Question 1058945: �
At first a runner jogs at 5 mph and then jogs at 8 mph traveling 7 miles in 1.1 hours. How long does the runner jog at each speed. (Hint: Let t represent the amount of time the runner jogs at 5 mph. Then 1.1 - t represents the amount of time the runner jogs at 8 mph.) Set up an equation for distance at 5 mph + distance at 8 mph = 7miles.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Make a data table and then use RT=D basic principle to form the necessary equations.

SPEED TIME DISTANCE SLOW 5 FAST 8 Total 1.1 7

You need to fill in the missing cells of the data table.

SPEED TIME DISTANCE SLOW 5 FAST 8 x 8x Total 1.1 7

The additional variable, x for the FAST time is the only way I can see to do this. You have two sums in the variables, t and x. They are LINEAR equations forming a system.

, and you should be able to solve this system.
Answer by ikleyn(52798) (Show Source): You can put this solution on YOUR website!
.
At first a runner jogs at 5 mph and then jogs at 8 mph traveling 7 miles in 1.1 hours. How long does the runner jog at each speed.
(Hint: Let t represent the amount of time the runner jogs at 5 mph. Then 1.1 - t represents the amount of time the runner jogs at 8 mph.)
Set up an equation for distance at 5 mph + distance at 8 mph = 7miles.
~~~~~~~~~~~~~~~~~~~~~

They just explained you how to start your solution:
So, I will start as they recommend:

"Let t represent the amount of time the runner jogs at 5 mph." "Then 1.1 - t represents the amount of time the runner jogs at 8 mph." During time "t" hours the runner jogs the distance of 5*t miles. During time 1.1-t hours the runner jogs the distance 8*(1.1-t) miles. In all, the runner will jog 5t + 8*(1.1-t) miles. Since it is 7 miles, you have this equation 5t + 8*(1.1-t) = 7. Simplify and solve for "t": 5t + 8.8 - 8t = 7, -5t = 7 - 8.8, -3t = -1.8, t = = 0.6. Hence, the runner jogs 0.6 hour = 36 minutes at 5 mph. The rest of time, 1.1 hour minus 0.6 hour = 0.5 hour = 30 minutes, the runner jogs t 8 mph.

Solved.

And forget on using tables (as "josgarithmetic" recommend) if you want to learn on how to solve such problems.

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