on a partly cloudy day, milton decides to walk back from work. when it is sunny, he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy, he increases his speed to ( s + 1 ) miles / hr. if his average speed for the entire distance is 2.8 miles / hr, what fraction of the total distance did he cover while the sun was shining on him? Select
A) 1 / 5 B) 1 / 6 C) 1 / 4 D) 1 / 7 E) 1 / 3
<gadget id="calculator">2.8 + 2.8</gadget>
<output>5.6</output>

<gadget id="calculator">2.8 + 5.6</gadget>
<output>8.4</output>

<gadget id="calculator">8.4 + 5.6</gadget>
<output>14</output>

<gadget id="calculator">14 / 2</gadget>
<output>7</output>

<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>

<result>D</result>
on a partly cloudy day, milton decides to walk back from work. when it is sunny, he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy, he increases his speed to ( s + 1 ) miles / hr. if his average speed for the entire distance is 2.8 miles / hr, what fraction of the total distance did he cover while the sun was shining on him?
divide(1, divide(add(add(2.8, add(2.8, 2.8)), add(2.8, 2.8)), const_2))
if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is 2 / 14 = 1 / 7 . answer : d