The distance of the college and home of Rajeev is 80km. One day he was late by 1 hour than the normal time to leave for the college, so he increased his speed by 4km/h and thus he reached to college at the normal time. What is the changed (or increased) speed of Rajeev?

Q: The distance of the college and home of Rajeev is 80km. One day he was late by 1 hour than the normal time to leave for the college, so he increased his speed by 4km/h and thus he reached to college at the normal time. What is the changed (or increa…

Let the normal speed be x km/h, then 80 x - 80 ( x + 4 ) = 1 ⇒ x 2 + 4 x - 320 = 0 ⇒ x (x + 20) - 16 (x + 20) = 0 (x + 20 ) (x - 16) =0 x = 16 km/h Therefore (x + 4) = 20 km/h Therefore increased speed = 20 km/h

28 km/h
30 km/h
40 km/h
20 km/h

Correct Answer: 20 km/h

Explanation:

Let the normal speed be x km/h, then

$\frac{80}{x} - \frac{80}{(x + 4)} = 1$

$\Rightarrow$ $x 2 + 4 x - 320 = 0$

$\Rightarrow$ x (x + 20) - 16 (x + 20) = 0

(x + 20 ) (x - 16) =0

x = 16 km/h

Therefore (x + 4) = 20 km/h

Therefore increased speed = 20 km/h

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