Question

Two semi trucks are driving loads from Chicago to Denver, distance of 1125 miles. First truck leaves at 8 AM, averages 50 mph. Second truck leaves at 9 AM, averages at 54 mph.

How much would the driver of the first truck have to increase her speed in order to arrive in Denver first?

Answer 1

the answer is "at least 1.53 mph" . But I don't know how to get to this.

Answer 2

You have to think about what is going on. (It helps to have already solved similar problems)

First truck leaves at 8 AM, averages 50 mph.
After one hour, the truck is 50 miles closer to Denver, so it has 1125 miles - 50 miles=
1075 miles to go

Answer 3

Second truck leaves at 9 AM, averages at 54 mph, and has 1125 miles to go

Just to get an idea of what is going on, I would figure out how long will it take the first truck to get to Denver, starting at 9 AM. use rate*time= distance, or
time = distance/rate
time = 1075/50= 21.5 hours

the second truck will take 1125/54 = 20.83 hours

so that says the second truck will get to Denver first.
unless the first truck speeds up

Answer 4

If we are the first truck, we say, "we are only allowed 20 and 5/6 hour to go 1075 miles"
now use rate* time = distance :
rate * 125/6 = 1075
(btw, 20.8333... and 125/6 and 20 and 5/6 are all the same number)
solve for rate r
\[ r \cdot \frac{125}{6} = 1075 \]

can you do that ?

Answer 5

51.6?

Answer 6

yes, that is what I got. the 1st truck was going 50, and it has to speed up to 51.6
so it must increase its speed by 1.6 mph

I don't think the answer can be 1.53 mph ??

Answer 7

or, maybe they are thinking what should the new speed be starting immediately?
i.e. at 8 AM the 1st truck has to get to denver in 20 5/6 hours
?

can you figure that out ?

Answer 8

I'll try. Thank you, though!

Answer 9

wait!, because the 1st truck starts 1 hour earlier, it has 21 and 5/6 hours

Answer 10

so the problem is distance = 1125 miles
rate is unknown
time is 21 and 5/6 hours = 131/6 hours
rate * 131/6 = 1125