SOLUTION: A car leaves a city and travels east at 50mph. an hour later another car traveling at 70 mph, leaves the same city in pursuit of the first car. FIND (a) how many hours will it

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A car leaves a city and travels east at 50mph. an hour later another car traveling at 70 mph, leaves the same city in pursuit of the first car. FIND (a) how many hours will it      Log On

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Question 42823: A car leaves a city and travels east at 50mph. an hour later another car traveling at 70 mph, leaves the same city in pursuit of the first car. FIND
(a) how many hours will it take the second car to overtake the first car.
I got 2.5 hours
(b) how many miles will the cars be from the city when they meet?
Answer by aaaaaaaa(138) About Me  (Show Source):
You can put this solution on YOUR website!
(a) If the car has already traveled 50 mph, then it is this many miles away, in x hours after the second car has left:
50+%2B+50x
While the second car:
70x
The distance must be equal when they meet, so we have 50+%2B+50x+=+70x
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=2.5.
  • Graphical form: Equation 50%2B50x=70x was fully solved.
  • Text form: 50+50x=70x simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+50%2B50x=70x+%29
    For tutors: simplify_cartoon( 50+50x=70x )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+50+%29%2B50%2Ax=70x.
Moved 50 to the right of expression
It becomes 50%2Ax%2Bhighlight_green%28+50+%29=70x.
Look at 50%2Ax%2B50=highlight_red%28+70%2Ax+%29.
Moved these terms to the left highlight_green%28+-70%2Ax+%29
It becomes 50%2Ax%2B50-highlight_green%28+70%2Ax+%29=0.
Look at 50%2Ax%2Bhighlight_red%28+50+%29-70%2Ax=0.
Moved 50 to the right of expression
It becomes 50%2Ax-70%2Ax%2Bhighlight_green%28+50+%29=0.
Look at highlight_red%28+50%2Ax+%29-highlight_red%28+70%2Ax+%29%2B50=0.
Eliminated similar terms highlight_red%28+50%2Ax+%29,highlight_red%28+-70%2Ax+%29 replacing them with highlight_green%28+%2850-70%29%2Ax+%29
It becomes highlight_green%28+%2850-70%29%2Ax+%29%2B50=0.
Look at %28highlight_red%28+50+%29-highlight_red%28+70+%29%29%2Ax%2B50=0.
Added fractions or integers together
It becomes %28highlight_green%28+-20+%29%29%2Ax%2B50=0.
Look at %28highlight_red%28+-20+%29%29%2Ax%2B50=0.
Removed extra sign in front of -20
It becomes %28-highlight_green%28+20+%29%29%2Ax%2B50=0.
Look at highlight_red%28+%28-highlight_red%28+20+%29%29%2Ax+%29%2B50=0.
Remove unneeded parentheses around factor highlight_red%28+20+%29
It becomes -highlight_green%28+20+%29%2Ax%2B50=0.
Look at highlight_red%28+-20%2Ax%2B50+%29=0.
Solved linear equation highlight_red%28+-20%2Ax%2B50=0+%29 equivalent to -20*x+50 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=2.5.

Universal Simplifier and Solver


Done!


So, the time the second car took is really 2.5 hours.
For b, just substitute 70x for x = 2.5 and you'll get 175 miles.