One motorcycle is travelling at a speed of #45mph# and the other motorcycle is travelling at a speed of #65mph# both starting at the same time. When they will be #385# miles apart?

Question

Autumn Arnold · Accepted Answer

If they are traveling in opposite direction, it will be #3 1/2# hours until the motorcycles are #385# miles apart. But if they are traveling in same direction, it will be #19 1/4# hours until the motorcycles are #385# miles apart.

Although some important details are not mentioned, we assume that (a) motorcycles start from the same point (b) the result could be different if they are traveling in opposite same direction As one motorcycle travels at a rate of #45mph# and other motorcycle travels in opposite direction at a rate of #65mph# In one hour the distance between them will be #45+65=110# miles and to be #385# miles apart they will take #385/110# = #(5xx7xx11)/(2xx5xx11)# = #(cancel5xx7xxcancel11)/(2xxcancel5xxcancel11)# = #7/2=3 1/2# hours. If the other motorcycle travels in same direction at a rate of #65mph# In one hour the distance between them will be #65-45=20# miles and to be #385# miles apart they will take #385/20# = #(5xx7xx11)/(2xx2xx5)# = #(cancel5xx7xx11)/(2xx2xxcancel5)# = #77/4=19 1/4# hours.

Roman Alvarez · Answer

undefined To find out when the two motorcycles will be 385 miles apart, you can use the formula for distance traveled, which is:

$$ \text{Distance} = \text{Speed} \times \text{Time} $$

Let's denote the time it takes for the motorcycles to be 385 miles apart as $ t $ (in hours).

For the first motorcycle traveling at 45 mph, its distance covered in time $ t $ is $ 45t $ miles.

For the second motorcycle traveling at 65 mph, its distance covered in time $ t $ is $ 65t $ miles.

When added together, the total distance covered by both motorcycles after time $ t $ is $ 45t + 65t = 110t $ miles.

Setting this equal to 385 miles:

$$ 110t = 385 $$

Solving for $ t $:

$$ t = \frac{385}{110} $$

$$ t = \frac{35}{10} $$

$$ t = 3.5 \text{ hours} $$

So, it will take 3.5 hours for the two motorcycles to be 385 miles apart.