Question

Dave walked to his friend's house at a rate of 4 mph and returned back biking at a rate of 10 mph. If it took him 18 minutes longer to walk than to bike, what was the total distance of the round trip?

I need help on it

Answer 1

4 miles

Explanation:

Walking:

Distance = d miles

Rate = 4 mph

Time = t hours

`d=4\cdot t`

Biking:

Distance = d miles

Rate = 10 mph

Time
`=t-(18)/(60)=t-0.3` hours (convert minutes to hours)

`d=10\cdot (t-0.3)`

Hence,

`4t=10(t-0.3)\\ \\4t=10t-3\\ \\4t-10t=-3\\ \\-6t =-3\\ \\6t=3\\ \\t=(3)/(6)=(1)/(2)=0.5\ hour`

Therefore, the distance to friend's house is

`d=4\cdot 0.5=2\ miles`

and the total distance of the round trip is

`2+2=4\ miles`