At 2:00 p.m. two cars start toward each other from towns 240 miles apart. If the rate of one car is 10 mph faster than the other, how fast does each car go if they meet at 5:00 p.m.?

If 3x represents the distance that the slower car traveled, then which expression represents the distance the faster car traveled?

Question

At 2:00 p.m. two cars start toward each other from towns 240 miles apart. If the rate of one car is 10 mph faster than the other, how fast does each car go if they meet at 5:00 p.m.?

If 3x represents the distance that the slower car traveled, then which expression represents the distance the faster car traveled?

anonymous · Answer

OK, at least we know that the towns are 240 miles apart. so the total distance of both cars traveled will always be 240 miles, no matter what. like if one of them was breaking down just out of town, well, then the other car will make the 220 other miles to meet, otherwise they can't meet.

so we know that both cars combined have traveled 240 miles in 3 hours. the combined speed of them was 240 miles in 3 hours.
$$(\frac{ mileage1}{ 3 hours } + \frac{mileage2 }{ 3 hours })\times 3hours=240 miles$$of course a mileage over time is equivalent  to a velocity in mph. the difference of the velocities was 10 mph, and the overall speed is 240 miles / 3 hours.

anonymous · Answer

this equation captures the problem with everything that we know inserted:$$[(basemph+10)+ (basemph) ]\times 3hours=240 miles$$

anonymous · Answer

3(240)

anonymous · Answer

is that the right eqation??????

anonymous · Answer

we can use x for the unknown velocity:

(x+10 + x) = 240/3

anonymous · Answer

on the left hand side, we have the contributions of the two cars. on the right hand side, we have the overall speed those equal

anonymous · Answer

i have no idea what u r doing....:(

anonymous · Answer

we know that the combined distance traveled was 240 miles, right? :)

anonymous · Answer

ya, i can c that but what i really need is an equation, my options are 3(240) and 3x + 30

anonymous · Answer

that aren't complete equations, what do the complete eqns look like?

anonymous · Answer

this is all they gave me those three but i know it is not the 2nd one
3(240)
3x + 10
3x + 30

anonymous · Answer

and hay i just need the equation that epresents the distance the faster car traveled..

anonymous · Answer

3x + 30

because it has the same "base speed" as the other car, and every hour, it makes 10 miles more than the other one :)
since it took 3 hours, it travels 3 x 10 miles more