Question 58

If I travel by bus, I reach my office 15 min late, and if I travel by car, I reach 10 min early. If the distance between my home and my office is 25 km, then the difference of the reciprocals of average speeds of the bus and the car, in second per metre is:

Solution

Speed by bus = $$\frac{25000}{900}=\frac{250}{9}\ \frac{m}{s}$$ (Since 1 km = 1000m and 1 min = 60s)

Speed by car = $$\frac{25000}{600}=\frac{250}{6}\ \frac{m}{s}$$

Average speed = $$\frac{2xy}{x+y}$$

2xy = $$2\times\ \frac{250}{9}\times\ \frac{250}{6}$$

x+y=$$\frac{250}{9}+\frac{250}{6}=\frac{1250}{18}$$

$$\frac{2xy}{x+y}$$ = $$\frac{100}{3}\ \frac{m}{s}$$

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