Question

the time taken, t, for a journey of fixed distance is inversely proportional to the average speed of travel, s. If the journey takes 2 hours 15 minutes travelling at an average speed of 50km/hour, how long will it take if the average speed is 27km/hour. Give your answer in hours and minutes​

Answer 1

`\huge{\color{red}{\fbox{\textsf{\textbf{Answer}}}}}`

4 hours 12 minutes

Explanation:

We need to convert time in hours by diving 15 by 60

`\sf 2 (15)/(60) \\ \\ \sf 2 (1)/(4)`

as it is mixed fraction we will convert into improper

`\sf ((2 * 4) + 1)/(4) \\ \\ \sf time = (9)/(4) hours`

Now we need to find distance

`\sf \green {distance = speed * time}`

Here speed is 50km/h

`\sf \implies distance = 50 * (9)/(4)km \\ \\ \sf \implies distance = (25 * 9)/(2)km \\ \\ \sf \implies distance = (225)/(2) km \\ \\ \sf \implies \red {distance = 112.5km}`

Now we have to have time at new speed at 27km/h

and distance is same

`\sf \pink{ time = (distance)/(speed) }`

Now substituting the value of speed and distance

`\sf \implies time = (112.5)/(27)`

Now we will remove point(.) from the distance by multiplying 10 with 27

`\sf \implies time = (1125)/(27 * 10) \\ \\ \sf \implies time = (41.6)/(10)`

now we will convert it into mixed fraction

`\sf \implies time = 4 (1)/(5) hours`

Now we will convert fraction hours into minutes by multiply with 60

`\sf \implies time = 4 \: hours \: (1)/(5) * 60 \: minutes \\ \\ \sf \implies \orange{ time = 4 \: hours \: 12 \: minutes}`