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Question

Ellen works for a high-speed rail company that wants to develop a new rail line. Ellen’s project is to find a train that is the second fastest in the world. The Shinkansen Bullet Train in Japan is reported to go as fast as 320 kilometers per hour. The TGV train in France can reach speeds of 89.44 meters per second. Explain to Ellen how to find what speed her new train must go to be the second fastest in this group. Then, find an appropriate speed for Ellen’s train in miles per hour and use the formula distance = speed • time to find how far the train can go in 2.5 hours. 

Answer 1

First you must convert these 2 rates into the same units so that you can compare them to see which is the fastest and which is currently the second fastest train in the world . I would convert to km/hr only because the second question wants you to answer something involving 2.5 hrs.

 

    A liitle trick in conversions because I always get confused do I multiply or divide by 1000 and 3600. If you look at the units, they sort of act like fractions, where the numerator of one cancels with the denominator of the other. For example,

12 rotations/min  * 60 min/hr * 24 hr/day = 17280 rotations/day. Do you see the minutes and hours sort of cancel out?

 

Units can also be inverted. 3 dollars/gallon is 3/1 dollars /gallon which is the same as 1/3 gallons/dollar. 

so im my car gets 22 miles/gal and I pay 3 dollars/gallon, notice the gal are both in the denominator. So I must invert one to get the new units.

22 miles/gal * 1/3 gallons /dollar gives me 7.3333 miles /dollar  which meams every 7.3333 miles I drive, it costs me a dollar.

 

Back to your problem.

89.44 meters/sec * 60 sec/min * 60 min/hr * 1/1000 km/meter = 321.984 km/hr. Do you see how I used the units as fractions to set up this expression?

 

So, now that your units are the same, the French train is almost 2 km/hr faster. So pick a number between 320 and 321.984. Choose what you like, I'll pick that my train goes 320.769 km/hr. So r*t=d, and in my case 320.769 * 2.5 = 801.9225 km = d.