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.

a. How far are they from Chicago when the second truck overtakes the first truck?
b. If each of the drivers stop for meals for a total of 3 hours, what time will it be in Chicago when each truck reaches Denver?
c. How much would the driver of the first truck have to increase her speed in order to arrive in Denver first?

Answer 1

I already found the two parameter equations:
50 t and 54(t-1) ... but now I don't know what to do. The answers to the questions are a) 675 miles; b) 9:30 AM, 8:50 AM; c) at least 1.53 mph . But I don't know how to get to these.

Answer 2

do you have to explain how u got your answer or is it multiple choice
?

Answer 3

I have to show my work

Answer 4

your equations are wrong slightly
first truck goes 50 miles before second so equation is 50(t+1)
second is 54t equate
t=50/4
distance =vel *time =50/4 *54 =675

Answer 5

how'd you get t=50/4?

Answer 6

(where'd the 4 come from?)

Answer 7

50(t+1)=54t
50t+50=54t
50=54t-50t=4t
t=50/4

Answer 8

Okay thanks. How about part b?

Answer 9

take truck 2 distance/speed =1125/54 =20.83 = 20 hrs 50 min +3 hrs stop time
=23 hrs 50 min add on when he left 9am =almost a whole day ie 8. 50
you do the rest

Answer 10

thats just for the second truck right?

Answer 11

okay I got the first truck's time

Answer 12

how about the last part? (part c)

Answer 13

@jamaica25

Answer 14

if truck (1) got the 50 mile start he would have 1075 miles still to go
truck (2) takes 20.83 hrs so truck(1) would would have to do 1075/ 20.83 hrs=52