Kahlil walks for 4 hours at the rate of x miles an hour. he stops an hour for lunch and then returns on a bus to his starting point. however, the bus travels at a speed 6 times that of his walking rate and follows a route that is twice as long. what is the total number of hours spent on the entire trip?

6⅓ hours (or 6 hours and 20 minutes)

Explanation:

For Khalil on foot;

Let;

Speed = x miles/hour

Time = 4 hours

Distance = D (miles)

Speed = distance/time

x = D/4

D = 4x miles

For Khalil on the bus;

The bus travels at 6 times his walking rate, therefore;

Speed = 6x miles/hour

Bus follows a route that is twice as long, therefore;

Distance = 2D (miles)

Time = T (hours)

Speed = distance/time

6x = 2D/T

Remember, from above, D = 4x

Therefore,

6x = 2(4x)/T

6x × T = 8x

T = 8x/6x

T = 4/3 hours = 1⅓ hours

Therefore time spent by khalil on the bus = 1⅓ hours or 1 hour, 20 minutes.

Total hours spent on entire trip = hours khalil spent walking + lunch hour + hours khalil spent on the bus

Total hours = 4 + 1 + 1⅓ = 6⅓ hours

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