SOLUTION: At 9:00am a truck leaves the truck yard and travels west at a rate of 45mi/hr. Two hours later, a second truck leaves along the same route, travelling at 75 mi/hr. When will the se

Question 113213: At 9:00am a truck leaves the truck yard and travels west at a rate of 45mi/hr. Two hours later, a second truck leaves along the same route, travelling at 75 mi/hr. When will the second truck catch up to the first?
What I have so far is this 45(x)=75(x+2). Would this be correct so far?
Thank you for your help,
Barb Neely
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Almost correct ... you are using the distance formula which says that the distance the first
truck travels is 45 mph times x hours. The second truck travels at a rate of 75 mph, but
it travels 2 hours less than x. So the time this second truck travels is x - 2, not x + 2.
.
When the two trucks are finally the side-by-side, they are equal distance from the starting point
so their two distances are equal. In equation form this is:
.
45x = 75(x-2)
.
Multiply out the right side and this equation becomes:
.
45x = 75x - 150
.
get rid of the -150 on the right side by adding +150 to both sides and the equation becomes
.
45x + 150 = 75x
.
Next get rid of the +45x on the left side by subtracting 45x from both sides and you have:
.
+150 = 30x
.
Finally solve for x by dividing both sides by 30 to get:
.
x = 150/30 = 5 hours
.
Adding 5 hours to 9:00 a.m. means that at 2:00 p.m. the second truck catches up to the first truck.
.
5 hours after it pulls out, the first truck has gone 45*5 = 225 miles. The second truck
leaves 2 hours later (at 11:00 a.m.) and in the 3 hours until 2:00 p.m. It goes 75*3 = 225 miles
from the starting point ... so the two trucks are equally as far from the starting point.
.
Another way you can look at this problem is to say that in the 2 hours the first truck travels
by itself it goes 90 miles. So it has a 90 mile head start. The second truck sets out at
11:00 a.m. and it is traveling 30 mph faster than the first truck. Therefore, each hour
it is on the road it will make up 30 miles. To make up the 90 mile difference, therefore,
it will be 3 hours after the second truck departs that it will catch up to the first truck.
So the time it catches up is 3 hours after 11:00 a.m. which again is 2:00 p.m.
.
Hope this helps you to understand the problem a little better.
.

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