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? pls answer asap

Total distance for round trip is 4 miles

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:

Calculating distance covered while walking:

distance = 1.2 + 4b ------- eqn 1

Calculating distance covered while using bike for return trip:

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

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

cheater

step-by-step explanation: