Two trains, old steamy and chug-a-lug, are 290 miles apart from each other and headed for the same station. they started toward the station at 8: 00 a. m. if they are both set to arrive at 10: 30 a. m. and old steamy is going 6.14 mph, how fast must chug-a-lug be going?

122.14 mph.

Step-by-step explanation:

Given : Two trains,Old Steamy and Chug-a-Lug,are 290 miles apart from each other and headed for the same station. They started toward the station at 8:00 a.m.

To Find: If they are both set to arrive at 10:30 a.m. and Old Steamy is going 6.14 mph, how fast must Chug-a-Lug be going?

Solution :

Speed of Old Steamy train = 6.14 mph

Train started at 8 a.m. and arrived at 10.30 a.m.

So, time of travel = 2.5 hours

So, distance traveled by Old Steamy train =

                                                                      =

                                                                      =

Since the total distance traveled by train Old Steamy is 15. 35 miles. This means Old steamy was standing before the Chug-a-Lug i.e. Chug-a-Lug was 290 miles behind the Old steamy

Distance traveled by Chug-a-Lug  is distance traveled by Old Steamy to the station plus the distance between the trains

Now, Distance traveled by Chug-a-Lug = 15.35+290 miles

                                                                 = 305.35

Since we are given that they started and ended at the same time . So, the the time of travel for both the trains will be same = 2.5 hours

So, speed of  Chug-a-Lug =

                                            =

                                            =

Hence the speed of the Chug-a-Lug train is 122.14 mph.