Total distance for round trip is 4 miles
Solution:
Given that Dave walked to his friend's house at a rate of 4 mph and returned back biking at a rate of 10 mph
To find: total distance of round trip
Speed of Dave walking to his friend's house = 4 mph
Speed of Dave biking from his friend's house = 10 mph
Given that it took him 18 minutes longer to walk than to bike
Let us frame a equation using a variable "b"
Time taken while in bike = "b" hours
time taken to walk = 18 minutes + b = (0.3 + b) hours
[to convert 18 minutes to hours, divide 18 by 60
]
The relation between time and distance and speed is given as:
[tex]distance = speed \times time taken[/tex]
Calculating distance covered while walking:
[tex]distance = 4 mph \times (0.3 + b) hours[/tex]
[tex]\text {distance }=1.2+4 \mathrm{b} \text { miles }[/tex]
distance = 1.2 + 4b ------- eqn 1
Calculating distance covered while using bike for return trip:
[tex]\text { distance }=10 \mathrm{mph} \times \text { b hour }[/tex]
distance = 10b miles -------- eqn 2
We know distance covered to travel friend house is same in both going and return trip
Hence we can equate eqn 1 and eqn 2
1.2 + 4b = 10b
6b = 1.2
b = 0.2
Thus Time taken while in bike = 0.2 hours
time taken to walk = (0.3 + b) hours = (0.3 + 0.2) = 0.5 hours
So total distance of round trip is given as:
total distance of round trip = eqn 1 + eqn 2 = 1.2 + 4b + 10b
total distance of round trip = 1.2 + 14b = 1.2 + 14(0.2) = 1.2 + 2.8 = 4
Thus total distance for round trip is 4 miles
