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. Use complete sentences and show your work.

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. Use complete sentences and show your work.

Answer 1

first, convert everything to the same units. I expect km/hr would be good here.

Japan: 320 km/hr
France: 89.44 m/min = 322 km/hr

So, any speed between those two would be second fastest.

Answer 2

do it yourself

Answer 3

To find the speed Ellen's new train must go to be the second fastest, she needs to compare the speeds of the Shinkansen Bullet Train and the TGV train.

First, convert the speed of the Shinkansen Bullet Train from kilometers per hour to meters per second. Since 1 kilometer is equal to 1000 meters and 1 hour is equal to 3600 seconds, we can calculate the speed as follows:

Speed (in meters per second) = 320 km/h * (1000 m/km) / (3600 s/h)

Simplifying the equation:

Speed = 320,000 m/3600 s
Speed ≈ 88.89 m/s

Now, Ellen can compare this speed to the speed of the TGV train, which is already given as 89.44 meters per second. Since she wants her train to be the second fastest, the speed of her train needs to be greater than 88.89 m/s but less than 89.44 m/s.

To find an appropriate speed for Ellen's train in miles per hour, we can convert the speed of the TGV train from meters per second to miles per hour. Since 1 mile is equal to 1609.34 meters and 1 hour is equal to 3600 seconds, we can use the following formula:

Speed (in miles per hour) = 89.44 m/s * (1 mile / 1609.34 m) * (3600 s / 1 hour)

Simplifying the equation:

Speed ≈ 198.83 miles per hour

So, an appropriate speed for Ellen's train would be approximately 198.83 miles per hour.

To find how far the train can go in 2.5 hours, we can use the formula: distance = speed • time.

Plugging in the values:

Distance = 198.83 miles/hour * 2.5 hours

Distance ≈ 497.07 miles

Therefore, Ellen's train can travel approximately 497.07 miles in 2.5 hours.