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A man travels from A to B at 4 km/h and from B to A at 6 km/h. The total journey takes...

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lucky092569 | (Level 3) Honors

Posted January 17, 2011 at 10:29 AM via web

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A man travels from A to B at 4 km/h and from B to A at 6 km/h. The total journey takes 45 minutes. Find the distance traveled.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted January 17, 2011 at 10:37 AM (Answer #1)

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Let the distance from A to B is D

Then, the distance from B to A is also D.

Let us use the distance formula to find D.

We know that:

D = Speed * Time

Given that the speed from A to B is S1 = 4

==> D = 4 * T1

Also given that the speed from B to A is S2 = 6

==> D = 6 * T2

Then D = D

==> 4T1 = 6T2 .............(1)

But we know that the total time is 45 min

==> 45 min = 3/4 hour.

==> T1 + T2 = 3/4

We will substitute into (1).

==> 4T1 = 6 ( 3/4 - T1)

==> 4T1 = 9/2 - 6T1

==> 10T1 = 9/2

==> T1 = 9/20 = 0.45 hour

==> T2 = 3/4 - 9/20 = 6/20 = 0.3 hour

Then D = 4*T1 = 4* 0.45 = 1.8 km

Then, the distance is 1.8 km.

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