Two cyclists start simultaneously towards each other from aurangabad and ellora, which are 28 km apart. an hour later they meet and keep pedalling with the same speed without stopping. the second cyclist arrives at ellora 35 minutes later than the first arrives at aurangabad. find the speed of the cyclist who started from ellora.
Answers
Lets say they meet at a point C which is x km away from aurangabad and (28 - x) km away from Ellora.
The distance covered by A is x Km and by B is (28 - x) km.
This is covered in 1 hrs so the speed for :
A = x km/h
B = (28 - x) km / h
A has (28 - x) km to cover whereas B has x km more to cover.
Since we have the distance and the speeds for the two, we can get the time taken to reach respective destinations.
A :
(28 - x) / x
B :
x /(28 - x)
We know that A arrives 35 minutes later which is equivalent to 7 / 12 hrs
Putting this in an equation form we have :
x / (28 - x) + 7/12 = (28 - x) / x
Expanding the equation we get :
12 x² + 196 x - 7x² = 9408 - 672x + 12x²
Collecting like terms together :
- 7x² + 868 x - 9408 = 0
Dividing through by a negative :
7x² - 868 x + 9408 = 0
Solving for X using the quadratic formula we have :
X = {868 +/-√(868² - 4 ×7 × 9408)} / (2 × 7)
X = {868 +/- (700)} / 14
X = 12 or 112
We pick 12 since 112 is more than the total distance thus it is unrealistic.
Speed of B is :
(28 - 12) = 16
16 m / s
Answer:
Explanation:
Let person A be the one moving from aurangabad and N moving from Ellora
Lets say they meet at a point C which is x km away from aurangabad and (28 - x) km away from Ellora.
The distance covered by A is x Km and by B is (28 - x) km.
This is covered in 1 hrs so the speed for :
A = x km/h
B = (28 - x) km / h
A has (28 - x) km to cover whereas B has x km more to cover.
Since we have the distance and the speeds for the two, we can get the time taken to reach respective destinations.
A :
(28 - x) / x
B :
x /(28 - x)
We know that A arrives 35 minutes later which is equivalent to 7 / 12 hrs
Putting this in an equation form we have :
x / (28 - x) + 7/12 = (28 - x) / x
Expanding the equation we get :
12 x² + 196 x - 7x² = 9408 - 672x + 12x²
Collecting like terms together :
- 7x² + 868 x - 9408 = 0
Dividing through by a negative :
7x² - 868 x + 9408 = 0
Solving for X using the quadratic formula we have :
X = {868 +/-√(868² - 4 ×7 × 9408)} / (2 × 7)
X = {868 +/- (700)} / 14
X = 12 or 112
We pick 12 since 112 is more than the total distance thus it is unrealistic.
Speed of B is :
(28 - 12) = 16
16 m / s