SOLUTION: Lois rode her bike to visit a friend. She traveled at 10 mph. While she was there, it began to rain. Her friend deve her home in the car traveling at 25 mph. Lois took 1.5 hours lo

Algebra ->  Expressions-with-variables -> SOLUTION: Lois rode her bike to visit a friend. She traveled at 10 mph. While she was there, it began to rain. Her friend deve her home in the car traveling at 25 mph. Lois took 1.5 hours lo      Log On


   

Question 1126491: Lois rode her bike to visit a friend. She traveled at 10 mph. While she was there, it began to rain. Her friend deve her home in the car traveling at 25 mph. Lois took 1.5 hours longer to go to her friend’s than to return home. How many hours did it take Lois to ride to her friends house?
Found 3 solutions by josgarithmetic, MathLover1, ikleyn:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Distance to or from was 25 miles.
Time to go to her friend at 10 mph was 2.5 hours. 
          SPEEDS      TIME      DISTANCE
TO           10        d/10       d
FROM         25        d/25       d
DIFF                   1.5


d%2F10-d%2F25=1.5
.
.
d=25

d%2F10:
25%2F10=highlight_green%282.5%29hours


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Alternative --- let t be time going to and then t-1.5 is time going back.
Same distance each way.
10t=25%28t-1.5%29
and gives the same result for t, 2.5 hours.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Lois rode her bike to visit a friend. She traveled at 10mph.
d=10mph%2At........eq.1
While she was there, it began to rain. Her friend drove her home in the car traveling at 25mph.

d=25mph%2At....eq.2
if Lois took 1.5 hours longer to go to her friend’s than to return home, we have
d=10mph%2A%28t%2B1.5%29......eq.1a
How many hours did it take Lois to ride to her friends house?
since distance equal,
10mph%2A%28t%2B1.5%29=25mph%2At
%28t%2B1.5%29=2.5%2At
t%2B1.5=2.5t
1.5=2.5t-t
1.5=1.5t
t=1
so, %28t%2B1.5%29=1%2B1.5=2.5-> hours did it take Lois to ride to her friends house

Answer by ikleyn(52765) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let "t" be the time biking.


Then the time by car is (t-1.5). It is the time in hours to return back, according to the condition.


Your equation is


    10*t = 25%2A%28t-1.5%29


saying that the each way distance is the same.


To solve the equation, multiply its both sides by 2. You will get


    20t = 50t - 75


    75 = 50*t - 20*t

    75 = 30*t  ====>  t = 75%2F30 = 150%2F60 of an hour =  2 hours and 30 minutes.   Answer


Check.  The distance "to there" by the bike = 10*2.5 = 25 miles.

        The distance back  = 25*(2.5-1.5) = 25 miles.   ! Correct !

Solved.

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