Question

You normally drive a 12-h trip at an average speed of 100 km/h . Today you are in a hurry. During the first two-thirds of the distance, you drive at 116 km/h
If the trip still takes 12 h, what is your average speed in the last third of the distance?

Answer 1

Answer:

78 km/h

Explanation:

If I normally drive a 12 hour trip at an average speed of 100 km/h, my destination has a total distance of:

• 100 km/h · 12 h = 1,200 km

Today, I drive the first 2/3 of the distance at 116 km/h. Let's first calculate what 2/3 of the normal distance is.

• 1,200 * 2/3 = 800 km

I've driven 800 km already. I need to drive 400 km more to reach my final destination. I need to figure out my average speed during this last 1/3 of the distance.

To do this, I first need to calculate how much time I spent driving 116 km/h for the past 800 km.

• 116 km/1 h = 800 km/? h
• 800 = 116 · ?
• ? = 800/116
• ? = 6.89655172

I spent 6.89655172 hours driving during the first 2/3 of the distance.

Now, I need to subtract this value from 12 hours to find the remaining time I have left.

• 12 h - 6.89655172 h = 5.10344828 h  

Using this remaining time and my remaining distance, I can calculate my average speed.

• ? km/1 hr = 400 km/5.10344828 h
• 5.10344828 · ? = 400
• ? = 400/5.10344828
• ? = 78.3783783148  

My average speed during the last third of the distance is around 78 km/h.