MATH SOLVE

4 months ago

Q:
# Stanley drives m miles in x hours. how many hours would he save if he drove the same distance at k miles per hour?

Accepted Solution

A:

The time saved will be: x - m/k
This is a simple exercise in manipulating symbols. Let's take a look at the problem and break it down.
"Stanley drives m miles in x hours"
This statement immediately gives us 2 variables; "m" to represent how many miles the trip is and "x" for the number of hours it took Stanley to drive that far. Now let's look at the next statement.
"How many hours would he save if he drove the same distance at k miles per hour?"
This statement gives us another variable "k" for a new speed and gives us the question to answer. How many hours would Stanley save if he made the trip at a different speed. Since we're interested in hours saved, we need 2 different time values. They are
1. How much time did Stanley originally take?
2. How much time will the new speed make Stanley take?
Looking at m, x, and k. We can immediately see that x is the original time that Stanley took. So we have that value. But we don't have any value for how long will it take at a new speed. But can we calculate it? And the answer to that is YES. The time it will take is the distance divided by the new speed. And that would be m/k. And since we're looking for savings, we just need to subtract the two time values. So our equation becomes
x - m/k
where
x = original time taken
m = distance of trip
k = new speed to drive at