Question 97397
speed=distance/time.


let distance=d
let t = time going
let T = time returning


going: 30 = d/t --> t = d/30
returning: 50 = d/T --> T = d/50


so t+T = d/30 + d/50


but we are told that the total time of the trip (ie t+T) is 8hours, so we have 8 = d/30 + d/50


so we have a fractional equation to solve. If we multiply every term by 150, we get
{{{ 150x8 = (150d)/(30) + (150d/50) }}} and now we can cancel the fractions, leaving
{{{ 1200 = 5d + 3d }}}
1200 = 8d
d = 1200/8
d = 150miles


cheers
Jon.