At 3: 30 p. m., berto’s train was 34 miles past the egg farm, traveling at an average speed of 85 miles per hour. at the same time on a nearby track, eduardo’s train was traveling at an average speed of 110 miles per hour and had 12 miles to go before it reached the egg farm. to the nearest hundredth of an hour, after how much time will the trains meet up?

a. 0.11
b. 0.25
c. 0.88
d. 1.84

  D.  1.84

Step-by-step explanation:

Eduardo's train is 46 miles behind Berto's train, but is traveling 25 mph faster. It will make up that 46 mile difference in ...

  (46 mi)/(25 mi/h) = 46/25 h = 1.84 h

Eduardo's train is 46 miles behind Berto's train, but is traveling 25 mph faster. It will make up that 46 mile difference in ...

 (46 mi)/(25 mi/h) = 46/25 h = 1.84 h

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.