Question 1195351: Bella and Regina both leave the mall at the same time, but in opposite directions. If Regina travels 5 mph faster than Bella and after 3 hours they are 87 miles apart, how fast is each traveling?
Found 3 solutions by ikleyn, math_tutor2020, Alan3354:
Answer by ikleyn(52772)   (Show Source):
You can put this solution on YOUR website! .
Bella and Regina both leave the mall at the same time, but in opposite directions.
If Regina travels 5 mph faster than Bella and after 3 hours they are 87 miles apart,
how fast is each traveling?
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Let r be the slower rate; then the faster rate is (r+5) mph.
The total separating distance in 3 hours is 3r + 3*(r+5) miles,
and it is equal to 87 miles. So your base equation is
3r + 3*(r+5) = 87 miles.
Simplify and find r
3r + 3r + 15 = 87
6r = 87 - 15 = 72
r = 72/6 = 12 miles per hour.
ANSWER. The Bella's rate is 12 mph.
The Regina rate is 12 + 5 = 17 mph.
CHECK. 3*12 + 3*17 = 36 + 51 = 87 miles separating distance in 3 hours. ! Correct !
Solved.
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- Travel and Distance problems
- Travel and Distance problems for two bodies moving in opposite directions
- Travel and Distance problems for two bodies moving in the same direction (catching up)
in this site.
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You will find the solutions of many similar problems there.
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Answer by math_tutor2020(3816)  (Show Source):
You can put this solution on YOUR website!
B = Bella's speed in mph
B+5 = Regina's speed in mph
The formula we'll need is:
distance = rate*time
often abbreviated as
d = r*t
The term "rate" is the same as "speed".
If Bella travels for 3 hours at a speed of B mph, then she travels a distance of...
d = r*t
d = B*3
d = 3B
If we knew what B was, then we could find a numeric distance for Bella.
Meanwhile, Regina also travels for 3 hours but at a speed of B+5 mph
d = r*t
d = (B+5)*3
d = 3B+15
Here are their distances:
Bella = 3B
Regina = 3B+15
These distances are in miles.
These two distances must add to 87 miles since this is the gap between them after the three hour mark.
It might help to draw out a number line diagram to visualize what's going on.
Have one person go left, and the other go right.
Bella + Regina = 87
(3B) + (3B+15) = 87
6B + 15 = 87
6B = 87-15
6B = 72
B = 72/6
B = 12
Bella's speed is 12 mph.
This is comparable to bike speed, though a bit on the slower side.
Perhaps Bella is riding up a slightly steep hill, or she may be biking at a somewhat leisurely pace not in a hurry to get anywhere.
Regina's speed is B+5 = 12+5 = 17 mph
If you wanted, you can calculate the distances of each person (now that we've determined the value of B). I'll leave that to you for practice.
Answers:
Bella's speed = 12 mph
Regina's speed = 17 mph
Answer by Alan3354(69443)  (Show Source):
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