Alright, lets get started.
Suppose the speed to the ranch = x mph
So, speed to the ocean will be = (x-4) mph (because the speed was 4 mph less than the speed to the ranch)
Distance to the ranch = 888 miles
time moving to the ranch [tex] = \frac{distance}{speed} [/tex]
time moving to the ranch [tex] = \frac{888}{x} [/tex]
time moving to the ocean [tex] = \frac{280}{x-4} [/tex]
As per given in question, the 888 mile trip to the ranch took three times as long as the 280 mile trip to the ocean , means
[tex] \frac{888}{x} = 3 * \frac{280}{x-4} [/tex]
[tex] \frac{888}{x}= \frac{840}{x-4} [/tex]
Corss multiplying
[tex] 888 (x-4) = 840 x [/tex]
[tex] 888 x - 3552 = 840 x [/tex]
[tex] 48 x = 3552 [/tex]
[tex] x=74 [/tex]
Hence speed to ranch = 74 mph
Hence speed to ocean = [tex] 74 - 4 = 70 [/tex] mph
time for trip to ranch = [tex] \frac{888}{74} = 12 [/tex] hrs
time for trip to ocean = [tex] \frac{280}{70} = 4 [/tex] hrs
So, speed to ranch is 74 mph and trip time is 12 hrs and speed to ocean is 70mph and time is 4 hrs.
Hope it will help :)
