Question

Places A and B are 56km apart on a highway. One car starts from A and another from B at
the same time. If the cars travel in the same direction at different speeds, they meet in 4 hours. If
they travel towards each other, they meet in one hour.

a.Taking the speed of car at A is x km/hr and that of car at B is y km/h. The equation that would
represent the situation algebraically (assume y>x) when the cars are travelling in opposite
direction

b.Taking the speed of car at A is x km/hr and that of car at B is y km/hr.The equation that would
represent the situation algebraically (assume y>x) when the cars are travelling in same direction

c.The speed of car at A is

d.The( speed of car A+ Speed of car B) is:

Answer 1

Step-by-step explanation:

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Answer 2

Given: distance between places A and B is 56 km.

Cars start from point A and B, if they travel in same direction the they meet in 4 hours and if they travel towards each other or in different directions then they meet in 1 hour.

Solution:

Assume that the speed of car at A is x and speed car at B is y.

Part a)

Write The equation that would  represent the situation algebraically (assume y>x) when the cars are travelling in opposite  direction.

$\[\begin{array}{l}y - x = \frac{{56}}{1}\\ \Rightarrow y - x = 56 - - - - - - \left( 1 \right)\end{array}\]$

Part b)

Write the equation that would  represent the situation algebraically (assume y>x) when the cars are travelling in same direction.

$\[\begin{array}{l}y + x = \frac{{56}}{4}\\ \Rightarrow 4y + 4x = 56 - - - - - - \left( 2 \right)\end{array}\]$

Part c)

Multi[ly equation (1) by 4.

$\[\begin{array}{l}\left( {y - x = 56} \right) \times 4\\ \Rightarrow 4y - 4x = 224 - - - - - - \left( 3 \right)\end{array}\]$

Solve equations (3) and (2).

$\[\begin{array}{l}\,\,\,\,\,\,\,4y - 4x = 224\\\underline {\left( + \right)4y + 4x = \,\,\,56} \\\,\,\,\,\,\,\,8y\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 280\end{array}\]$

$\[\begin{array}{l} \Rightarrow 8y = 280\\ \Rightarrow y = \frac{{280}}{8}\\ \Rightarrow y = 35km/h\end{array}\]$

Find the speed of car at A by putting the speed of car at B ( value of y) in equation (1).

$\[\begin{array}{l}y - x = 56\\ \Rightarrow 35 - x = 56\\ \Rightarrow x = 91km/h\end{array}\]$

Part d)

Find the sum of speeds of both the cars.

$\[91 + 35 = 126km/h\]$

Hence, The( speed of car A+ Speed of car B) is $126 km/h.$