Question 1140094: How do I figure when two motorcycles will meet when they are 196 apart, one is going 65 mph one is going 75 mph I figured the time for both riders but how do I figure when they will meet?
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! r * t = d
r = rate
t = time
d = distance
the distance between the motorcyclists is equal to 196 miles.
the rate for one of the motorcyclists is equal to 65 miles per hour.
the rate for the other motorcyclist is equal to 75 miles per hour.
the time that each motorcyclist travels has to be the same.
since the total distance is 196 miles, one of the motorcyclists will travel x miles and the other motorcyclist will travel 196 - x miles.
you can choose for yourself which one travels x miles and which one travels 196 - x miles.
note that the total distance traveled by both will be 196 miles because x + 196 - x = 196.
the general formula is, once again, r * t = d
your formula for the first motorcyclist becomes:
65 * t = x
your formula for the second motorcyclist becomes:
75 * t = 196 - x
these two equations need to be solved simultaneously so the value of x and t will be the same in both equations.
the trick is to make one of the variables disappear so that you can solve for the other variable.
once you find the value of the other variable, you can use that value to find the value of the variable that disappeared.
this is standard procedure for solving equations simultaneously.
there are several ways to do it.
here's a reference on how to solve equations simultaneously.
https://www.purplemath.com/modules/systlin1.htm
i'm going to solve this one by substitution.
your two equations are:
65 * t = x
75 * t = 196 - x
in the first equation,solve for t to get t = x / 65
in the second equation, replace t with x / 65 to get:
75 * x / 65 = 196 - x
multiply both sides of this equation by 65 to get:
75 * x = 65 * (196 - x)
simplify to get:
75 * x = 12740 - 65 * x
add 65 * x to both sides of this equation to get:
75 * x + 65 * x = 12740
combine like terms to get:
140 * x = 12740
solve for x to get:
x = 12740 / 140 = 91
when x = 91, the first equation becomes 65 * t = 91
solve for t to get t = 91 / 65 = 1.4
when x = 91, the second equation becomes 75 * t = 196 - 91
combine like terms to get:
75 * t = 105
solve for t to get t = 105 / 75 = 1.4
the time each traveled is the same, as it should be.
the first motorcyclist traveled 91 miles.
the second motorcyclist traveled 105 miles.
they met when they both traveled 1.4 hours.
if you figured the time for both riders, they you must have had 1.4 hours for each.
the actual time that they met could be anything, depending on when they both started.
1.4 hours is equal to 1 hour and 24 minutes.
if they both started at 10:00 am, they they met at 11:24 am.
if you looking for the number of miles that each traveled when they met, that would be 91 miles for the first rider and 105 miles for the second rider.
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
Without any information about the time they started, you can't find the time when they will meet. But from the given information it is easy to find how long it will take them to meet; so I will assume that is what you are asking for.
Their combined speed is 140mph; the distance between them initially is 196 miles. The time it takes them to meet is distance divided by rate:
It takes them 1.4 hours, or 1 hour 24 minutes, to meet.
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