Hi.
We are trying to find out how fast the cars are moving. The word for that is "speed." Now, to figure out speed, we have to multiply the distance the car traveled by the time it was traveling:
s = dt
Here, we know don't have a number for speed for either car. Instead, we have to compare the speed of the two cars:
s1 = speed of the faster car = unknown
s2 = speed of the slower car = unknown, but 5 mph slower than s1, so s2 = s1 - 5
We want to know time of travel, right? So we are going to manipulate that speed formula a little bit:
t = d / s
So t1 = d1 / s1 and t2 = d2 / s2.
where t1 is the time the faster car was traveling, s1 is the speed at which the faster car was moving, d1 is the distance the faster car traveled, t2 is the time the slower car traveled, s2 is the speed at which the slower car was moving, and d2 is the distance the slower car traveled.
Let's substitute values.
Since t1 = d1 / s1 and t2 = d2 / s2 and the time each car traveled is equal, we can do this:
d1 / s1 = d2 / s2
Then we can plug in the values we have:
268 / s1 = 248 / s1 - 5
Next, we cross multiply (because these are two ratios):
268(s1-5) = 248s1
268s1 - 1,340 = 248s1
20s1 = 1,340
s1 = 67 mph
Thus, the faster car was traveling 67 miles per hour.
The second (slower) car traveled at (s1 -5), so s2 is 62 miles per hour.
Now we can figure out the time it took for the cars to get to their destination:
t = s / d
Remember, the time of travel for each car was the same, so we can use the values for s1 and d1 OR for s2 and d2. Just don't mix them up! I'll choose to use s1 and d1.
t1 = d1 / s1
t1 = 268 miles / 67 miles per hour
t1 = 4 hours
Since t1 = t2, the second (slower) car must also have been traveling for four hours. So t2 = 4 hours, too.
Let's check to make sure the numbers work:
t2 = d2 / s2
4 hours = 248 miles / 62 miles per hour
That is true! Our answer must be correct.
