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

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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)   (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:

While the second car:

The distance must be equal when they meet, so we have
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


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

DETAILED EXPLANATION

Look at .
Moved 50 to the right of expression
It becomes .
Look at .
Moved these terms to the left highlight_green%28+-70%2Ax+%29
It becomes .
Look at .
Moved 50 to the right of expression
It becomes .
Look at .
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 .
Look at .
Added fractions or integers together
It becomes .
Look at .
Removed extra sign in front of -20
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+20+%29
It becomes .
Look at .
Solved linear equation highlight_red%28+-20%2Ax%2B50=0+%29 equivalent to -20*x+50 =0
It becomes .
Result:
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.
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