Question

Two buses leave a station at the same time and travel in opposite directions. One bus travels 15kmfaster than the other.hIf the two buses are 543 kilometers apart after 3 hours, what is the rate of each bus?kmRate of the faster bus:Rate of the slower bus:

Answer 1

Given:

a.) Two buses leave a station at the same time and travel in opposite directions.

Let,

Speed of Bus A = s

Speed of Bus B = s + 15

b.) The two buses are 543 kilometers apart after 3 hours.

d = 543 km

t = 3 hrs.

We get,

`\text{ (Speed Bus A)(t) + (Speed of Bus B)(t) = 543 km}`
`\text{ (v)(3) + (v + 15)(3) = 543 km}`
`\text{ }\frac{\text{(v)(3) + (v + 15)(3)}}{\text{ 3}}\text{ = }\frac{\text{543 km}}{\text{ 3}}`
`\text{ v + v + 15 km/h = 181 km/h}`
`\text{ 2v = 181 km/h - 15 km/h}`
`\text{ 2v = 166 km/h}`
`\text{ }\frac{\text{2v}}{\text{ 2}}\text{ = }\frac{\text{166 km/h}}{\text{ 2}}`
`\text{ v = }83\text{ km/h}`

Therefore,

the speed of the slower bus = 83 km/h

the speed of the faster bus = 83 km/h + 15 km/h = 98 km/h