On a 100 km track ,a train travels the first 30km at a uniform speed of 30km per hour. How fast must the train travel the next 70km so as to average 40km per hour for the entire trip

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Solution

Given:
Distance traveled in first part $d_{1}$ = 30 km
Distance traveled in second part = $d_{2}$ = 70 km

We know,
$T i m e = \frac{D i s t a n c e}{S p e e d}$
So for the first part $T i m e (t_{1}) = \frac{30}{30} = 1 h o u r$
Now,
We know,
$A v e r a g e s p e e d = \frac{T o t a l d i s t a n c e}{T o t a l t i m e} = \frac{d_{1} + d_{2}}{t_{1} + t_{2}}$
Putting all the values
$40 = \frac{100}{1 + t_{2}}$
Or, $t_{2} = 1.5 h$

Now.
Speed for the second part = $S p e e d = \frac{D i s t a n c e}{T i m e} = \frac{70}{1.5}$
After solving
Speed for the second part = 46.67 km/h

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a) A train travels a distance with a speed of 40 km/h and returns with a speed of 60 km/h. Calculate the average speed of the train.

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