Question

The road that connects the place A to the place B is straight in the first part and the rest is downhill. The bicyclist arrived from place A to place B in 1 hour and 15 minutes. When returning, it took him half an hour more. On a straight part of the road he was riding 4 km/h faster than uphill. Riding downhill is twice as fast as riding uphill and 50% faster than on a straight part of the road. What is the distance between A and B?​

Answer 1

Answer:

Given, Time taken to cover distance between place A & B = 1 hour 30 min = 1+

2

1

=

2

3

hour

Distance between A & B = 6 cm

Now speed of man =

time

Distance

=

3/2

6

=

3

2×6

[speed = 4 km/h]

solution

Answer 2

Given:

The road that connects place A to place B is straight in the first part and the rest is downhill. The bicyclist arrived from place A to place B in 1 hour and 15 minutes. When returning, it took him half an hour more. On a straight part of the road, he was riding 4 km/h faster than uphill. Riding downhill is twice as fast as riding uphill and 50% faster than on a straight part of the road.

To Find:

What is the distance between A and B?​

Solution:

Let the speed on the uphill road be x then the speed on the straight road will be (x+4) because it is said that he was riding 4km/hr faster in the straight road than uphill and the speed downhill will be 2x and also it is said that speed downhill is 50% faster than on straight path, so we can formulate,

$(x+4)+50%(x+4)=2x\\2x+8+x+4=4x\\x=12km/hr$

So, on the straight path speed is (x+4)=12+4=16km/hr

Uphill is 12km/hr and downhill is 24km/hr

Now, let the distance of the straight path be 'a' and of the hill be 'b', using the time information we can formulate two-equation as,

$\frac{a}{16} +\frac{b}{24} =1.25$

and,

$\frac{a}{16} +\frac{b}{12} =1.75$

Now solving both equations we will have the values of (a,b) as (12,12)

So the total distance will be,

$distance=a+b\\=12+12\\=24km$

Hence, the distance between A and B is 24km.