Places a and b are 80 km apart

Asked by admin @ 25/08/2021 in Math viewed by 285 People

places A and B are 80km apart from each other on a high way . A car starts from A and another car starts from B at the same , if they move in the same time they meet in 8 hours and if they move in opposite direction they meet in 1 hour and 20 minutes, find the speed of the care,

Answered by admin @ 25/08/2021

Answer:

Speed of car A = 35 kmph & that of B = 25 kmph

To find:

Find the speed of the car = ?

Solution:

Let two cars A and B are separated by 80 km apart.

Let speed of A be x km/hr and speed of B be y km/hr

Distance to be travelled = 80 km

If the cars A and B moves in the same time, both the cars will meet together in 8 hours.

This can be written as

$\begin{array} { c } { \text {Distance} = \text {Speed} \times \text { Time } } \\\\ { \quad 80 = ( a - b ) \times 8 } \\\\ { a - b = \frac { 80 } { 8 } } \\\\ { a - b = 10 \ldots \ldots ( 1 ) } \end{array}$

If the cars A and B moves in opposite direction, both the cars will meet together in 1 hour and 20 minutes.

This can be written as

$\begin{array} { c } { 80 = ( a + b ) \times \left( \frac { 80 } { 60 } \right) } \\\\ { 80 = ( a + b ) \times \left( \frac { 4 } { 3 } \right) } \\\\ { \quad 80 \times \frac { 3 } { 4 } = ( a + b ) } \\\\ { a + b = \frac { 240 } { 4 } } \\\\ { a + b = 60 \ldots \ldots ( 2 ) } \end{array}$

Solving equation (1) & (2), we get

$\begin{array} { c } { a + b = 60 } \\\\ { a - b = 10 } \\\\ { 2 a = 70 } \\\\ { a = \frac { 70 } { 2 } } \\\\ { a = 35 \mathrm { kmph } } \end{array}$

Putting a = 35 kmph in equation (1), we get,

$\begin{array} { c } { a + b = 60 } \\\\ { 35 + b = 60 } \\\\ { b = 60 - 35 } \\\\ { b = 25 } \\\\ { b = 25 \mathrm { kmph } } \end{array}$

Speed of car A = 35 kmph & that of B = 25 kmph

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Places a and b are 80 km apart

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