SOLUTION: Carlos takes 20 minutes longer than Erica does to make the 240-mile drive between two cities. Erica drives 3 miles an hour faster. How fast do Carlos and Erica drive?
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Question 1026740: Carlos takes 20 minutes longer than Erica does to make the 240-mile drive between two cities. Erica drives 3 miles an hour faster. How fast do Carlos and Erica drive?
The rest of the unit involved matrices and so I am sure that is required to solve this one too, but I do not fully understand how to work this problem. Thank you. Found 3 solutions by josgarithmetic, stanbon, MathTherapy:Answer by josgarithmetic(39630) (Show Source):
You can put this solution on YOUR website! Carlos takes 20 minutes longer than Erica does to make the 240-mile drive between two cities.
Is this a uniform work-rates problem or a travel rates problem?
No matter. Erica drives 3 miles an hour faster. How fast do Carlos and Erica drive?
Try as a uniform travel rates problem, since rates of movement are given.
RT=D to relate rate as speed, time, and distance.
Make a data table.
Variable assignments are implied here; and hour is 20 minutes.
rate time distance
Carlos r t+1/3 240
Erica r+3 t 240
Totals?
Thinking ahead some, matrices do not appear to be very useful. The solution process should involve a term or equation using , so this would suggest not a linear system.
The system taken initially from the tabulated description:
Simplification of the system:
Two equations involving
This indicates two equal expressions for : ------This should be very very, very useful.
A way to form two LINEAR equations to solve the problem seems absent. Also it seems unreasonable so having found a simple relationship between r and t, JUST SUBSTITUTE for r into both simplified equations of the system; and solve either or both for t. You should expect the same value for t using either equation.
You can put this solution on YOUR website! Carlos takes 20 minutes longer than Erica does to make the 240-mile drive between two cities. Erica drives 3 miles an hour faster. How fast do Carlos and Erica drive?
===
Carlos DATA:
dist = 240 miles ; rate = r mph ; time = 240/r hrs
----
Erica DATA:
dist = 240 miles ; rate = r+3 mph ; time = 240/(r+3) hrs
----------
Equation::
Carlos time = Erica time + 1/5 hr
------------------------------------
240/r - 240/(r+3) = 1/5
========
5*240r + 5*240*3 - 5*240r = r(r+3)
------
r^2 + 3r - 15*240 = 0
r = 58.52 mph (Corlos rate)
f+3 = 61.52 mph (Erica rate)
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Cheers,
Stan H.
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You can put this solution on YOUR website! Carlos takes 20 minutes longer than Erica does to make the 240-mile drive between two cities. Erica drives 3 miles an hour faster. How fast do Carlos and Erica drive?
The rest of the unit involved matrices and so I am sure that is required to solve this one too, but I do not fully understand how to work this problem. Thank you.
Let Carlos’ speed be S
Then Erica’s is: S + 3
We then get the TIME equation: ------->
240(3)(S + 3) = 240(3S) + S(S + 3) --------- Multiplying by LCD, 3S(S + 3)
(S - 45)(S + 48) = 0
S, or Carlos’ speed = OR S = - 48 (ignore)
Erica’s speed: 45 + 3, or
It's as SIMPLE as that!
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