Question 1095657: Jose can drive his car 50 mph and cover a certain distance in 20 minutes less than when he drives at 45 mph. Find that distance. Found 3 solutions by ankor@dixie-net.com, ikleyn, greenestamps:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Jose can drive his car 50 mph and cover a certain distance in 20 minutes less than when he drives at 45 mph.
:
change 20 min to 1/3 hr
let t = time required at 45 mph
then = time at 50 mph
:
Write a distance equation; dist = speed * time
45t = 50(t - 1/3))
45t = 50t -
45t - 50t =
-5t =
multiply both sides by -3
15t = 50
t = 50/15
t = 3 hrs at 45 mph
then
3 hrs = time required at 50 mph
"Find that distance "
50 * 3 = 150 mi
:
:
:
Check the distance at 45 mph
45 * 3.333 = 150 mi also
Literal translation of the condition to a Math equation is this:
Let D be the distance under the question. Then
= .
Here D/45 is the time spent at the rate 45 mph;
D/50 is the time spent at the rate 50 mph;
and = of an hour = 20 minutes is the time difference, given by the condition.
To solve, multiply both sides by 450 to get
10*D - 9*D = 150,
which implies D = 150 kilometers.
You can put this solution on YOUR website! There are always many different ways of solving a problem. You have received two responses showing perfectly good solutions to your problem. Look how much different the two methods are; and compare the level of effort required in each one.
And now look at another solution, found be starting with a different interpretation of the given information.
"Jose can drive his car 50 mph and cover a certain distance in 20 minutes less than when he drives at 45 mph. Find that distance."
Of course you need to change the 20 minutes to 1/3 hour, since the speeds are in miles per hour.
Then re-phrase the given information like this:
"50 mph for some number of hours t is equal to 45 mph for (t+1/3) hours"
50 mph for 3 hours makes 150 miles.
This solution is, of course, very nearly the same as given in the first response you got to your question. Unfortunately, his choice of a variable led to an equation involving fractions, which resulted in more work to reach the answer.
The lesson to learn from this is that you should always be open to trying different methods for solving any particular type of problem. You might find that one of the methods just "works" for you better than any others....
