A car travels 382 miles in 8 hours. The first part of the trip, through the mountains, the car's speed is 42mph, and the second part the car's speed is 58mph. It took ? hours the first part of the trip. Round to the nearest tenth. I need someone to explain a solution to finding the answer to this problem. And please explain every step of your solution to the end, and why you are doing your solution the way you are doing it.

Question

A car travels 382 miles in 8 hours.  The first part of the trip, through the mountains, the car's speed is 42mph, and the second part the car's speed is 58mph.  It took ? hours the first part of the trip.  Round to the nearest tenth.  I need someone to explain a solution to finding the answer to this problem.  And please explain every step of your solution to the end, and why you are doing your solution the way you are doing it.

mathteacher1729 · Answer

Let's change the numbers but keep the idea the same. 

A car travels 200 miles in 4 hours. It was going 65mph for the first part of the trip, and 85mph for the 2nd part of the trip.  How long was each part of the trip? 

The key here is to set up a system of equations: 

"65 mph for x hours plus 85 mph for y hours means we've traveled 382 miles." 

65x + 85y = 382


"the time spent driving was 4 hours"

x+y = 4

Can you see what to do next?

anonymous · Answer

Let time take for the first part of the trip = x

Distance traveled for first part of the trip = 42 * (x)

Distance traveled for the second part of the trip = 58 * (8-x)

Sum of the distance = 382 

So 42x + 58(8-x) = 382
Solve for x

anonymous · Answer

Formula used: Distance = Speed x Time

anonymous · Answer

jgeorge, I know the formula, just can't see how it applied to this problem.  Where did you get the 8-x in your equation?

anonymous · Answer

total time taken  = 8 hours 
time taken for the first half = x 
so time taken for the second half = total time - time taken for the first half
 = 8 - x

Is that okay?

mathteacher1729 · Answer

indiana -- did my answer help?

anonymous · Answer

mathteacher...your answer did help some...I did not think of using 2 different variables in the equation, for each leg of the journey...

anonymous · Answer

But I guess I was looking more for an equation that used the same variable, which is how jgeorge did it, and it makes more sense to me.

anonymous · Answer

A negative number divided by a negative number equals a positive number, right?

anonymous · Answer

Yep

mathteacher1729 · Answer

Cool, whichever method works best for you -- go for it! :D

anonymous · Answer

Thanks jgeorge...mathteacher1729....I will be using this sight extensively...I'm majoring in nursing.  :)