Question

I travel the first part of the journey at 40 kmph and the second part at 60 kmph and cover the total distance of 240 km to my destination in 5 hours. How long did the first part of my journey last?
A) 4 hours
B) 2 hours
C) 3 hours
D) 2 hours 24 minutes

Answer 1

Hint: First assume the time taken at 40 kmph. Then, find the distance covered for the first part by the distance formula, Distance = Time /Speed. After that find, the distance traveled in the second part also. After that add both distances and equate to 240 km. Then do some simplification to get the distance travelled in the first part.

Complete step-by-step answer:
Given: - Total distance = 240 km
Total time = 5 hours
Speed during first part = 40 kmph
Speed during second part = 60 kmph
Let the time taken in the first part be x hr and in the second part be (5 - x) hr.
Then, the distance covered in the first part is,
$ \Rightarrow 40x$ km……………….. (1)
Also, the distance covered in the second part is,
$ \Rightarrow 60\left( {5 - x} \right)$ km ………...….. (2)
As total distance covered is 5 hours.
So, add equation (1), (2) and equate it to 240 km,
$ \Rightarrow 40x + 60\left( {5 - x} \right) = 240$
Open bracket and multiply the term,
$ \Rightarrow 40x + 300 - 60x = 240$
Move the constant part on the right side,
$ \Rightarrow 40x - 60x = 240 - 300$
Subtract the like terms,
$ \Rightarrow - 20x = - 60$
Divide both sides by -20,
$\therefore x = 3$
So, the first part of the journey lasts for 3 hours.

Hence, option (C) is correct.

Note: Speed and distance are directly proportional. For a constant amount of time, with increase in speed, distance covered increases and with decrease in speed, distance covered decreases.
Speed and time are inversely proportional. For a constant distance, with increase in speed, time decreases and with decrease in speed, time increases.