SOLUTION: Suppose you need to move many tonnes of gravel and you have two trucks available. One truck is capable of completing the job in 15 trips, while the other truck is capable of comple

Question 826357: Suppose you need to move many tonnes of gravel and you have two trucks available. One truck is capable of completing the job in 15 trips, while the other truck is capable of completing the job in 25 trips.To solve the following questions, notice that one truck completes 1/15 of the job each trip and the other truck completes 1/25 of the job each trip.
a. How much of the job is completed if the two trucks make one trip together?
b. How many trips are required to complete the job if the two trucks travel together?
c. Suppose that one truck can complete the job in (n) trips and the other truck can complete the job in 120 trips. Write an equation to represent the total number of trips, (T), required if the two trucks work together.
d. If 55 trips are required when the two trucks in question c. work together, how many trips would it take for the first truck to complete the job alone?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
One truck is capable of completing the job in 15 trips, while the other truck is capable of completing the job in 25 trips.
To solve the following questions, notice that one truck completes 1/15 of the job each trip and the other truck completes 1/25 of the job each trip.
:
a. How much of the job is completed if the two trucks make one trip together?
+ =
The common denominator is 75
+ = * 100 = 10.67% completed
:
b. How many trips are required to complete the job if the two trucks travel together?
Let t = no. of trips to complete job
Let the completed job = 1
+ = 1
multiply equation by 75 to clear the denominators
5t + 3t = 75
8t = 75
t = 75/8
t = 9.375 ~ 10 trips of the two trucks required
However in the interest of economy, have the smaller truck make 10 trips
and larger truck make 9 trips
+ =
+ = 1, exactly a complete job
:
c. Suppose that one truck can complete the job in (n) trips and the other truck can complete the job in 120 trips.
Write an equation to represent the total number of trips, (T), required if the two trucks work together.
+ = 1
multiply by 120n, results:
120t + tn = 120n
t(120+n) = 120n
t =
:
d. If 55 trips are required when the two trucks in question c. work together, how many trips would it take for the first truck to complete the job alone?
= 55
120n = 55(120+n)
120n = 6600 + 55n
120n - 55n = 6600
65n = 6600
n = 6600/65
n ~ 101 trips for the 1st truck alone
:
:
Check this
+ = 1.00, a complete job
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