Respuesta :
Answer:
182 miles.
Step-by-step explanation:
Given:
Two trains move between two towns.
Time taken by first train = 2 hr 48 minutes =
Change minute into hour:
60 minute = 1 hour
1 minute = [tex]\frac{1}{60}[/tex]
48 minutes = [tex]\frac{1}{60}\times48=\frac{48}{60} =0.8\ hour[/tex]
Time taken by first train in hour = [tex]2+0.8=2.8\ hours[/tex]
Time taken by second train = 4 hr 40 minutes
Similarly, 40 minutes = [tex]\frac{40}{60} =0.67\ hour[/tex]
Time taken by second train in hour = [tex]4+0.67=4.67\ hours[/tex]
The rate of the first train is 26 mph more than that of the second train.
Question asked:
What is the distance between these towns ?
Solution:
Let speed of second train = [tex]x\ miles\ per\ hour[/tex]
As the speed of the first train is 26 mph more than that of the second train.
Speed of first train = [tex]26+x\ miles\ per\ hour[/tex]
As two trains move between two towns means distance traveled by both train is same.
By using : [tex]Distance=speed\times time[/tex]
Distance traveled by first train = Distance traveled by second train
[tex]speed\times time[/tex] =
[tex](26+x)2.8=x\times4.67[/tex]
[tex]26\times2.8+x\times2.8=4.67x\\72.8+2.8x=4.67x\\[/tex]
Subtracting both sides by [tex]2.8x[/tex]
[tex]72.8=1.87x[/tex]
Dividing both sides by 1.87
[tex]x=38.93[/tex]
Speed of second train = 38.93 miles per hour
[tex]Distance=speed\times time[/tex]
= 38.93 [tex]\times[/tex] 4.67
= 181.80 miles.
Thus, the distance between these towns is 182 miles (nearest whole number).
