A tourist was planning a trip by car for travelling at some constant speed for 2.5 hours. However, he found that if he increases the speed by 20 km/h he can cover the same distance in 30 minutes less time than it was planned. What was the planned speed of the tourist, in km/h?

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eudora eudora · Answer 1 · 2019-01-11T22:42:50+01:00

Answer:

The planned speed of the tourist is 80 km per hour.

Step-by-step explanation:

Let the constant speed of a tourist be v km per hour and distance covered be x km.

Now we will start forming the equations as per the direction given in the question.

Since tourist covers x km with a constant speed of v in 2.5 hours.

So the equation will be speed v = Distance covered (x)÷Time taken(2.5)hours

Therefore v = x÷2.5

⇒ x = 2.5v-------(1)

Now we form the second equation

With a new speed (v+20) = Distance (x)÷Time(2.5-0.5)

Or v+20 = x÷2

⇒ now we multiply 2 on both the sides of this equation

⇒ 2(v+20) = x-------(2)

Now we put the value of x from equation (2) to equation number (1)

⇒ 2(v+20) = 2.5v

⇒ 2v+40 = 2.5v

⇒ 2.5v-2v = 40

⇒ 0.5v = 40

⇒ v = 40÷(0.5) = 80 km/hr