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

Question

badhi · Answer

Firs u can find the time when the second driver reaches Denver (take $t'$)

First driver will have to at least arrive at this time (t') to fullfill the requirement.

if the required speed increase - $u$

$(50+u)(t'-8)=1125$

For certain it should be less than 4

anonymous · Answer

that still doesn't explain how it gets to at least 1.53, @BAdhi

kropot72 · Answer

The times taken for the journey by the second truck is 1125/54 hours. To arrive at the same time as the second truck the first truck must travel at a speed of:
$$\large \frac{1125}{1+\frac{1125}{54}}\ mph$$

kropot72 · Answer

*The time taken........

anonymous · Answer

that equals 51.53

kropot72 · Answer

Correct. Therefore the speed of the first truck must increase from 50 mph to more than 51.53 mph, giving a required increase in speed of more than 51.53 - 50 = 1.53 mph.

anonymous · Answer

Oh okay. Thank you!

kropot72 · Answer

You're welcome :)

anonymous · Answer

Refer to the attached solution from Mathematica 9.