Question 1039834: Can someone please help me with this word problem
From a point on a straight road, Chris and Elena ride bicycles in the same direction. Chris rides at 10 mph and Elena rides at 14 mph. In how many hours will they be 30 mi apart?
Found 2 solutions by josmiceli, Theo:
Answer by josmiceli(19441)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! chris rides at 10 miles an hour.
elena rides at 14 miles per hour.
in how many miles will they be 30 miles apart.
rate * time = distance.
rate is in miles per hour.
time is in hours.
distance is in miles.
for chris, the formula becomes 10 * time = distance.
fo4r elena, the formula becomes 14 * time = distance.
you want to know when the distance between them will be 30 miles.
since they will have been riding the same time when they are 30 miles apart, we'll let T = the time they both took.
we'll let D1 = distance that chris rides and D2 = distance that elena rides.
formula for chris becomes 10 * T = D1
formula for elena becomes 14 * T = D2
we know that we want the distance between them to be 30 miles, and we know that elena will have been riding the most miles, so we get D2 - D1 = 30
Since D2 = 14 * T and D1 = 10 * T, then D2 - D1 = 50 becomes 14 * T - 10 * T = 30.
factor out the T to get (14 - 10) * T = 30.
simplify to get 4 * T = 30
divide both sides of the equation by 4 to get T = 30 / 4 = 7.5 hours.
to see if we did this correctly, we replace T with 7.5 in the original equations to get:
rate * time = distance.
for chris, formula becomes 10 * 7.5 = 75 miles.
for elena, formula becomes 14 * 7.5 = 105 miles.
the difference between the miles that elena rides and the miles that chris rides is 30 miles.
this confirms the solution is correct.
the solution is they will be 30 miles apart in 7.5 hours.
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