Story problem

Question

Carrie was on a long 258 mile road trip. The first part of the trip there was lots of traffic, she only averaged 19 mph. The second part of the trip there was no traffic so she could drive 44 mph. If the trip took her 7 hours, how long did she travel at each speed?

Answer 1

Here it is Jess:

 

Let's call the number of hours at 19 mph "a" and the number of hours at 44 mph "b"

 

Now, we know 2 things about these numbers:

 

1) those hours add up to 7, so a + b = 7

 

2) the distance traveled at the 2 different speeds adds up to 258 miles, so "a" hours at 19 mph + "b" hours at 44 mph = 258, so 19a + 44b = 258

 

Now, since the first equation tells us that a + b = 7, it's also true that b = 7 - a, which means we can stick "7 - a" any place we see b.

 

Which means we can have 19a + 44(7 - a) = 258

 

Continue by distributing the middle part, so 19a + 308 - 44a = 258

 

Continue by combining terms, so - 25a = - 50, which means that 25a = 50, which means....

 

a = 2. The number of hours traveled at 19 mph (which we called "a") is 2, and therefore the number of hours traveled at 44 mph (which we called "b") is 5.

 

Check it: (19 x 2) + (44 x 5) = 258 ?

 

38 + 220 = 258 ?

 

258 = 258 CHECK, woo hoo!

 

Hope this helps, and that it's in time for school on Tuesday. :-)

 

Cheers,

 

Matt in NY