28. An aeroplane covered a distance of 400 km at an average speed of x km/h.
On the return journey, the speed was increased by 40 km/h. Write down an expression
for the time taken for :
(i) the onward journey,
(ii) the return journey.
If the return journey took 30 minutes less than the onward journey, write down an
equation in x and find its value.
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Answer:
(i) Time taken for the onward journey = 400/x hours.
(ii) Time taken for the return journey = 400/x + 40 hours.
According to the question,
⇒ 400/x + 40 = 400/x – ½
⇒ 800x = 800(x + 40) – x(x + 40)
⇒ x2 + 40x – 32000 = 0
⇒ (x + 200)(x – 160) = 0
⇒ x = - 200 (inadmissible) or 160
Hence, the required value of x is 160.
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