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sergiy2304 [10]
2 years ago
7

Jonathan increased his rate of walking by 25% at halfway to his destination and therefore arrived half an hour earlier than was

planned. How long did it take for Jonathan walk to his destination?O
Mathematics
1 answer:
Flura [38]2 years ago
5 0

Answer:

1.67 hours

Step-by-step explanation:

Let the original speed of Jonathan = x units/hr

Let the original time taken by Jonathan = y hours

Let the distance = D units

Formula for distance is given as:

Distance = Speed \times Time

Given that half the distance is covered by original speed.

\Rightarrow \dfrac{D}{2} = \dfrac{x}{2}\times \dfrac{y}{2}\\\Rightarrow D = \dfrac{xy}{2} ..... (1)

Half the distance is covered by increasing the rate by 25%.

i.e. increased speed:

\dfrac{5}{4}x\ units/hr

Hence, Time taken:

\dfrac{y}{2}-\dfrac{1}{2}

Distance traveled is half of the total distance:

\Rightarrow \dfrac{D}{2} = \dfrac{5x}{4}\times (\dfrac{y}{2}-\dfrac{1}{2})\\\Rightarrow D = \dfrac{5x}{2}\times (\dfrac{y}{2}-\dfrac{1}{2}) .... (2)

Dividing (1) by (2):

\dfrac{xy\times 4}{2\times 5x(y-1)} = 1\\\Rightarrow 2y=5y-5\\\Rightarrow 3y=5\\\Rightarrow y =1.67\ hours

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