Math Problem x5

Question

Monique is 69 miles away from Kayla. They are traveling towards each other. If Kayla travels 9 mph faster than Monique and they meet after 3 hours, how fast was each traveling?

Answer 1

K = 9 + M

3K + 3M = 69 (time times speed = distance)

3(9+M) + 3M = 69

27+3M +3M = 69

6M = 69-27 = 42

M = 42/6 = 7 mph

K =9+7= 16 mph

3(16+7) = 3(23) = 69 miles

Answer 2

You don't need to know how far each girl traveled to find out their speeds. You only have to realize that they will not run past each other, so in total they travel 69 miles. Doesn't matter who did what part of that 69 miles.

This helps tremendously because we have a total distance (69 miles) and a total time to go that distance (3 hours). Since Speed = Distance / Time, we can imagine the girls' total speed together will equal their total distance divided by their total time. So we use the equation:

Total speed = 69mi/3hr

Total speed = 23 mi/hr

We need to write an expression that models their total speed to solve for each individual girl. Remember that Kayla goes 9 mi/hr faster than Monique? Say M is Monique's speed and (M+9) is Kayla's speed. So their total speed together is M + (M + 9). In other words, their total speed is 2M + 9

Now put that total speed (2M + 9) = their total speed value of 11.5 mi/hr and solve for M:

2M + 9 = 23

Use algebra (subtract on both sides, divide on both sides). Now you have Monique's speed. Add 9 to Monique's speed to find Kayla's speed.

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