Problema Solution
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 provided by our tutors
The Shinkansen Bullet Train in Japan has a speed of
320 kilometers per hour = 320 km/h = 320*10^3 m/(60*60)s = 800/9 = 88 8/9 m/s = 88.89 m/s
since 1 km = 1000 m and 1 h = 60*60 s
The TGV train in France can reach speeds of 89.44 meters per second or written in short 89.44 m/s
let 'v' be the the speed of Ellen's train, since this train is the second fastest we have the following inequalities
88 8/9 < v < 89.44
the speed v needs to be in the interval (88 8/9, 89.44)
we can take v = 89 m/s (since 88. 8/9 < 89 <89.44)
lest covert m/s to miles/h
1 m = 0.000621371 miles
1s = 1/3600 hours
1 m/s = 0.000621371/ ( 1/3600) miles/h
1 m/s = 2.2369 miles/h
v = 89 m/s = 89*2.2369 miles/h
v = 199.1 miles/h
t = 2.5 h
d = v*t
d = 199.1 * 2.5
d = 497.75 miles
the distance of the second fastest train traveling with 89 m/s or 191.1 miles/h will be 497.75 miles.