Question

If Lance Armstrong cycles at 10km/hr, then he arrives at certain destination at 1 pm. If he cycles at
15km/hr, he will arrive at same place at 11 a.m. At what speed must he cycle to get there by noon?
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Answer 1

Hi,

Answer:

Let’s assume,

The distance covered by Lance Armstrong be “d” km  

and  

The time taken by him to reach the destination by noon be “t” hr

So,  

Time taken when he cycles at 10 km/hr = (t + 1) hr

Time taken when he cycles at 15 km/hr = (t - 1) hr

Now,

When he cycles with a speed of 10 km/hr and reach the destination at 1 p.m., the equation for speed is given by

10 = d/ (t + 1)

⇒ d = 10 t + 10 …… (i)

And,

When he cycles with a speed of 15 km/hr and reach the destination at 11 a.m., the equation for speed is given by

15 = d / (t - 1 )

⇒ d = 15t - 15 ….. (ii)  

From equation (i) & (ii), we get

15t - 15= 10t + 10

⇒ 5 t = 25

⇒ t = 5 hours

Substituting the value of t in equation (i), we get

d = 10*5 + 10 = 50+10 = 60 km

Thus,

To reach the destination by noon he must cycle with a speed of,

= 60 / 5  

= 12 km/hr

Hope this is helpful!!!!