Corey drives 14 miles per hour slower than Cheryl. They started at the same spot, and drove in opposite directions. After 5.7 hours, they were 478.8 miles apart. Find each car’s speed.

Answer 1

Hey Karinna K.,

Given that Corey's speed is based off of Cheryl's, let's use the variable x to represent the miles that Cheryl is moving. We can now set up two equations which represent Cheryl and Corey's speeds.

1. Cheryl's speed = x miles/hour
2. Corey's speed = (x-14) miles/hour

We should note here that the numerator represents distance while the denominator represents time. So if we want to know the accumulative distance that they both traveled after a certain amount of hours, we would simply add the fractions together:

1. (x miles/hour) + (x-14 miles/hour) = (2x-14 miles/hour)

(knowing the accumulative distance in the terms of x will be helpful for solving for x as we already know the accumulative distance is 478.8 miles)

Now we must multiply our accumulative speed per hour by time and set this equal to the accumulative distance travelled so we can later isolate x:

1. (2x-14 miles/hour) * 5.7 hours = 478.8 miles
2. (11.4x-79.8) miles = 478.8 miles

Let's solve for x

1. (11.4x) miles = 478.8+79.8 miles
2. x = (478.8+79.8)/11.4 miles
3. x = 49 miles

Now that we have solved for x we can plug this back into our original two equations to find out how many miles per hour each person was going.

1. Cheryl's speed = (49) miles/hour
2. Corey's speed = (35) miles/hour

I hope that this answers your question. If you have any further confusion, just let me know.