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

Answer:

4 miles

Step-by-step explanation:

Walking:

Distance  = d miles

Rate = 4 mph

Time = t hours

$d=4\cdot t$

Biking:

Distance = d miles

Rate = 10 mph

Time $=t-\dfrac{18}{60}=t-0.3$ hours (convert minutes to hours)

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

Hence,

$4t=10(t-0.3)\\ \\4t=10t-3\\ \\4t-10t=-3\\ \\-6t =-3\\ \\6t=3\\ \\t=\dfrac{3}{6}=\dfrac{1}{2}=0.5\ hour$

Therefore, the distance to friend's house is

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

and the total distance of the round trip is

$2+2=4\ miles$