Question 127370: two trains are 276 miles apart, and their speeds differ by 10mph. they are traveling towards each other and will meet in 3 hours. find the speed of the slower train
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Start by letting x represent the speed of one of the trains and y represent the speed of the
other. The problem tells you that the two trains have speeds that are different by 10 mph.
In other words, if you subtract the two speeds, the answer will be 10 mph. In equation form
this is:
.
x - y = 10
.
This is the first equation that we need.
.
Next we use the distance formula. The distance a train travels is equal to the speed of
the train times the amount of time the train travels at that speed. Note that the trains each
travel for 3 hours. Therefore, the distance each travels during that time is its speed times 3.
.
So the distance one train travels is x times 3 and the distance the other train travels is
y times 3. If you total these two distances they must add up to be 276 miles, the distance
between them before they meet. In equation form this is:
.
3x + 3y = 276
.
This is the second equation we need.
.
Now return to the first equation, and let's solve for one of the unknown speeds in terms of
the other. For example we can solve for x by adding y to both sides of the equation. On
the left side the -y cancels the y we are adding and on the right side the y we are adding
appears. So, when we add y to both sides of the first equation, that equation is transformed
to:
.
x = 10 + y
.
Since x and 10 + y are equal, we can go to the second equation and substitute 10 + y for x
and then the second equation becomes:
.
3*(10 + y) + 3y = 276
.
Multiply out the left side by multiplying 3 times each of the terms in the parentheses
to get:
.
30 + 3y + 3y = 276
.
Add together the two terms that contain y and the sum is 6y. This makes the equation
become:
.
30 + 6y = 276
.
Get rid of the 30 on the left side by subtracting 30 from both sides. When you take away
30 from both sides the equation is reduced to:
.
6y = 246
.
Solve for y by dividing both sides of this equation by 6 since 6 is the multiplier
of y. Dividing both sides by 6 changes the equation to:
.
y = 246/6 = 41
.
Now we know that the speed of one train is 41 mph. We can find the speed of the second train
by substituting 41 for y in either of the two original equations and then solving the
resulting equation for x. The easier equation to use in this case is the first equation in
which we had:
.
x - y = 10
.
Substitute 41 for y and this becomes:
.
x - 41 = 10
.
Solve for x by adding 41 to both sides. On the left side the -41 is canceled out by the added 41.
On the right side you have 10 + 41 and the resulting equation is
.
x = 51
.
So the other train is going at 51 mph
.
Check the answers. Is there 10 mph difference in their speeds? Sure is. Then at 51 mph
for 3 hours one of the trains goes 3*51 = 153 miles. And at 41 mph for 3 hours the other
train goes 3*41 = 123 miles. So the total distance the trains travel is 153 +123 = 276 miles,
the distance they had to go before they meet. This checks also, so our two answers are
correct. One of the trains is going at 51 mph and the other is going at 41 mph.
.
Hope this helps you to understand the problem and a way that you can use to solve it.
.
|
|
|
