SOLUTION: Richard had to arrive at the airport at exactly 10 am. If he is able to drive at an average speed of 60 miles per hour he would arrive early at 9 am. If he drives at an average spe

Question 508371: Richard had to arrive at the airport at exactly 10 am. If he is able to drive at an average speed of 60 miles per hour he would arrive early at 9 am. If he drives at an average speed of 40 miles per hour he would arrive late at 11am. How fast should he travel to arrive at the airport at 10 am exactly?
You need to assume that Richard sets out at the same time in each scenario. You are not told what this time is and are not asked for it, but could work it out from the information given. You are asked to work out what his average speed should be if, after setting out at the same time as in the first two examples, he is to arrive exactly on time.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Richard had to arrive at the airport at exactly 10 am.
If he is able to drive at an average speed of 60 miles per hour he would arrive early at 9 am. If he drives at an average speed of 40 miles per hour he would arrive late at 11am.
How fast should he travel to arrive at the airport at 10 am exactly?
:
Let d = the distance
Let s = the speed required to arrive on time
:
Write a time equation for each scenario
- = 1 hr (early)
- = 1 hr (late)
:
Multiply by a common denominator in each to clear the denominator
60d - ds = 60s; multiplied by 60s
and
ds - 40d = 40s; multiplied by 40s
Arrange these two equation for elimination
+60d - ds = 60s
-40d + ds = 40s
-------------------adding eliminates ds leaving us with
20d = 100s
Divide both sides by 20
d = 5s
Using the 1st equation replace d with 20s
- = 1 hr
5 - = 1
- = 1 - 5
- = -4
Cancel 5 into 60
- = -4
multiply both sides by -12;
s = -12*-4
s = +48 mph is the required speed to arrive on time
:
:
Find the distance and check the solution in the 2nd equation
d = 5(48)
d = 240 mi
- = 1 hr
6 hrs - 5 hrs = 1 hr

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