Select the correct answerIf Abhi travels a certain distance at 6 km/hr, he reaches his destination 12 minutes early, but if he travels at 4 km/hr, he reaches his destination 10 minutes late. The speed (in km/hr) at which he should travel to reach his destination on time is?

Let's solve this step by step:

1. Let's denote the distance Abhi needs to travel as 'd' (in km) and the time he needs to reach his destination on time as 't' (in hours).

2. According to the problem, if Abhi travels at 6 km/hr, he reaches his destination 12 minutes early. This means that the time it takes him to travel the distance 'd' at 6 km/hr is 't - 12/60' hours (we divide by 60 to convert minutes into hours). So, we can write the first equation as: d = 6 * (t - 12/60).

3. Similarly, if Abhi travels at 4 km/hr, he reaches his destination 10 minutes late. This means that the time it takes him to travel the distance 'd' at 4 km/hr is 't + 10/60' hours. So, we can write the second equation as: d = 4 * (t + 10/60).

4. Now we have a system of two equations with two variables ('d' and 't') that we can solve. Since both equations are equal to 'd', we can set them equal to each other and solve for 't': 6 * (t - 12/60) = 4 * (t + 10/60).

5. Solving this equation gives us the value of 't' (in hours).

6. Once we have 't', we can substitute it back into either of the original equations to find 'd'.

7. Finally, to find the speed (in km/hr) at which Abhi should travel to reach his destination on time, we divide the distance 'd' by the time 't'.

Let's solve the equation from step 4:

6t - 6*(12/60) = 4t + 4*(10/60) 6t - 1.2 = 4t + 0.67 6t - 4t = 1.2 + 0.67 2t = 1.87 t = 1.87 / 2 t = 0.935 hours

Substitute t = 0.935 into the first equation: d = 6 * (0.935 - 12/60) d = 6 * (0.935 - 0.2) d = 6 * 0.735 d = 4.41 km

Finally, to find the speed at which Abhi should travel to reach his destination on time, we divide the distance 'd' by the time 't': Speed = d / t Speed = 4.41 km / 0.935 hr Speed = 4.72 km/hr

So, Abhi should travel at a speed of approximately 4.72 km/hr to reach his destination on time.

To solve this problem, we need to set up two equations based on the information given.

Let's denote:

• D as the distance Abhi needs to travel,
• T as the time it should take him to reach his destination on time,
• 6 km/hr as his faster speed, and
• 4 km/hr as his slower speed.

From the problem, we know that:

1. If he travels at 6 km/hr, he arrives 12 minutes early. So, D = 6(T - 12/60) (we convert minutes to hours by dividing by 60).

2. If he travels at 4 km/hr, he arrives 10 minutes late. So, D = 4(T + 10/60).

We can set these two equations equal to each other and solve for T:

6(T - 12/60) = 4(T + 10/60)

Solving this equation gives T = 1 hour.

Substitute T = 1 into the first equation to find D:

D = 6(1 - 12/60) = 5 km.

So, to reach his destination on time, Abhi should travel at a speed of D/T = 5 km/hr.