SOLUTION: Hi tutors here at algebra.com you've made my day happy. I just wanna ask this problem: " A car travels 60 miles in the same time that a car travelling 10 miles per hour faster t

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Question 1044581: Hi tutors here at algebra.com you've made my day happy. I just wanna ask this problem:
" A car travels 60 miles in the same time that a car travelling 10 miles per hour faster travels 90 miles. What is the rate of each car?"
Thanks for answering this problem
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
Travel Rates Rule, RT=D to relate rate, time, distance. 

               RATE        TIME       DISTANCE

SLOWCAR        r           t          d

FASTCAR       r+k          t          D

system%28k=10%2Cd=60%2CD=90%29


system%28d%2Fr=t%2CD%2F%28r%2Bk%29=t%29

d%2Fr=D%2F%28r%2Bk%29

d%28r%2Bk%29=Dr

dr%2Bdk=Dr

dr-Dr=-dk

Dr-dr=dk

r%28D-d%29=dk

highlight%28r=%28dk%29%2F%28D-d%29%29--------purely symbolic formula answer. Use the assigned values to evaluate r.

Answer by ikleyn(52858) About Me  (Show Source):
You can put this solution on YOUR website!
.
Hi tutors here at algebra.com you've made my day happy. I just wanna ask this problem:
" A car travels 60 miles in the same time that a car travelling 10 miles per hour faster travels 90 miles. What is the rate of each car?"
Thanks for answering this problem
~~~~~~~~~~~~~~~~~~~~ 

Your equation is

60%2Fu = 90%2F%28u%2B10%29,

where "u" is an unknown rate/speed of the car in the first scenario.

Multiply both sides by %28u%2A%28u%2B1%29%29%2F30. You will get

2*(u+10) = 3u,  or

2u + 20 = 3u,  or

20 = 3u - 2u,  or

u = 20.

Answer.  The rate of the 1-st car is 20 mph. The rate of the second car is 30 mph.

Be happy.


Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!
Hi tutors here at algebra.com you've made my day happy. I just wanna ask this problem:
" A car travels 60 miles in the same time that a car travelling 10 miles per hour faster travels 90 miles. What is the rate of each car?"
Thanks for answering this problem 
Let speed (rate) of slower car be S

Then speed (rate) of faster car = S + 10

Time slower car takes to cover 60 miles: 60%2FS

Time faster car takes to cover 90 miles: 90%2F%28S+%2B+10%29

We then get the following TIME equation: 60%2FS+=+90%2F%28S+%2B+10%29

90S = 60(S + 10)------ Cross-multiplying

90S = 60S + 600

90S - 60S = 600

30S = 600

S, or speed (rate) of slower car = 600%2F30, or highlight_green%28matrix%281%2C2%2C+20%2C+mph%29%29 

Add 10 to this speed (rate) to get speed (rate) of faster car.