Flying at 300 km/h John can go from his city to New York in 2 hours. If the speed is increased by 30% and a new route that is 10% longer taken how long will it take John.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

Speed is the distance traveled in unit time. If John travels at 300 km/h, he travels 300 km in one hour. The time taken by John to reach New York traveling at 300 km/h from his city is 2 hours. The total distance traveled by him in this duration of time is 300*2 = 600 km.

If he travels at a speed that is 30% faster, his speed is 300*1.3 = 390 km/h. The route that he uses when traveling at the higher speed is 10% longer. This gives the total distance traveled by him as 600*1.1 = 660 km.

The time taken by John to reach New York in the second case is equal to `660/390 ~~ 1.6923` hours

atsuzuki's profile pic

atsuzuki | (Level 1) Adjunct Educator

Posted on

The speed of the plane says how far it can go in a given time. In our case, it says 300 km/h, that is, i can go 300 km in one hour. Assuming this speed to be constant, that is, it is the same at any time, on the second hour (2hours) it flew to 2 times 300 km or 600 km. Since 2 hours is the time John needs to go from his city to New York, it simply means that his city is located 600 km from New York. If he takes another plane which is faster than the first by 30%, it means that the new speed is

`v = 300 ((km)/h) + (30*300)/(100) ((km)/h)=390 ((km)/h).`

This means that this plane can fly 390 km in one hour. However, this second plane uses a route that is 10% longer than the previous one, so the distance is

`d=600 km + (10*600)/(100) km = 660 km.`  

Now it is a question of doing proportion rule calculation as follows:

`390 kmharr 1 hour`

`660 km harr t`

Then 

`390 km* t = 660 km*1h rArr t= (660 km *1 h)/(390 km)=22/13 ((km)/h)` . 

This can be worked out a little bit more and written as

`t=1 9/(13) h.`

Since each hour has 60 minutes, 

`9/13 h = (9*60)/(13) min~=42 min`

Then, John's new travel time is about 1 hour and 42 minutes long.

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