Mike and adam left a bus terminal at the same time and traveled in opposite directions. mike's bus was in heavy traffic and had to travel 20 mi/h slower than adam's bus. after 3 hours, their buses were 270 miles apart. how fast was each bus going?

Adam's bus speed = a

mike's bus speed = m

total distace = t

m = a - 20

after 3 hour:

3 * (m + a) = t

3 * (m + a) = 270

3m + 3a = 270

[ 3 * (a - 20) ] + [ 3 * a ] = 270

[ 3a - 60 ] + 3a = 270

3a - 60 + 3a = 270

3a + 3a = 270 + 60

6a = 330

their speed:

a = 55

m = 55 - 20 = 35