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Question

At 10:00, Angela starts from her home and runs at a constant pace to Kathleens house, which is exactly 2 miles away. Immediately, she and Kathleen turn around and walk back to Angelas house exactly 4 miles an hour slower than Angela ran. When they arrive at Angelas house, the time is 10:45. At what speed did Angela run?

A
6 miles per hour
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B
6.5 miles per hour
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C
7 miles per hour
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D
7.5 miles per hour
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E
8 miles per hour
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Solution

The correct option is E 8 miles per hour
Let speed of angle be 'x' miles/hr.
Distance between Angela and Kathleens house =2 miles
Time taken by Angela to reach Kathleens house =2x
A.T.Q.
2x+2x4=4560
2(x4)+2xx(x4)=34
(4x8)4=3(x24x)
16x32=3x212x
3x228x+32=0
3x224x4x+32=0
3x(x8)4(x8)=0
(x8)(3x4)=0
x=8, x=43
Here x=43 is rejected [x4 will be less than 0 if ere x=43.
x=8
Therefore, speed of Angela is 8 miles/hr.

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