### Need of Speed For Average Speed

A man drives

**1 mile**to the top of a hill at**15 mph**. How fast must he drive**1 mile**down the other side to average**30 mph**for the 2-mile trip?**Here is calculation of that speed needed!**Something to tease your brain!

Showing posts with the label mile

- Get link
- Other Apps

- Get link
- Other Apps

A man drives 1 mile to the top of a hill at 15 mph. That means he took, 1/15 hours i.e

To achieve average speed of

Let

30 = 2/(1/15 + 1/x)

(1/15 + 1/x) = 2 / 30 = 1/15

1/x = 0

To conclude, it's impossible to achieve average speed of 30mph in trip.

- Get link
- Other Apps

If a car had increased its **average **speed for a **210** mile journey by **5**
mph, the journey would have been completed in** one hour **less. What was
the **original **speed of the car for the journey?

**Here is the calculation of averages speed!**

- Get link
- Other Apps

Let

As

D/S1 - D/S2 = 1 hr.

Here, D = 210 miles, S2 = S1 + 5,

210/S1 - 210/(S1+5) = 1

210(S1+5) - 210s = 1S1(S1+5)

S1^2 + 5S1 - 1050 = 0

(S1-30)(S1+35) = 0

Since speed can't be negative,

Hence, the original speed is 30 mph and average speed is 30 + 5 =

With the original speed it would have taken 210/30 =

- Get link
- Other Apps

You and I have to travel from Startville to Endville, but we have
only **one bicycle** between us. So we decide to **leapfrog**: We’ll leave
Startville at the same time, you **walking **and I **riding**. I’ll ride for **1**
mile, and then I’ll leave the bicycle at the side of the road and
continue on **foot**. When you reach the **bicycle** you’ll ride it for **1** mile,
passing me at some point, then leave the **bicycle** and continue **walking**. And
so on — we’ll continue in this way until we’ve both reached the
destination.

Will this**save** any time?

You say**yes**: Each of us is riding for part
of the distance, and riding is **faster** than walking, so using the bike
must increase our average speed.

I say**no**: One or the other of us is **always walking**; ultimately every
inch of the distance between Startville and Endville is traversed by
someone on foot. So the total time is unchanged — leapfrogging with the
bike is no better than walking the whole distance on foot.

Who’s right?

**Look who is right in the case! **

Will this

You say

I say

Who’s right?

- Get link
- Other Apps

That's going to save time for sure.

Let's assume that the distance between Startville and Endville is

tells only half story.

Yes, ultimately every inch of the distance between Startville and Endville is traversed by someone on foot but the distance that each of us walk is equal though different parts of journey. And for the rest of distance we ride on bicycle where total time required for journey is saved.