A family, planning a weekend trip, decides to spend not more than a total of 8 hours driving. By leaving early in the morning, they can average 40 miles per hour on the way to their destination. Due to the heavy Sunday traffic, they can average only 30 miles per hour on the return trip. What is the farthest distance from home they can plan to go?

• Time = Distance/Speed
  
  The total time allowed is 8 hours.
  
  The distance to the destination should be equal to the distance from the destination back home. We take the distance in each direction as x.
  
  The average speed to the destination is 40mph. The distance is x miles. Therefore using the formula that Time = distance / speed, the time taken for the forward journey will be x/40.
  
  The average speed of the return journey is 30mph. The distance will be the same which is x. Using the same formula, the time taken for the return journey is x/30.
  
  Since the total time taken for both trips cannot be more than 8 hours, we assume that they utilized the entire 8 hours. That means that the time taken for both journeys should be 8 hours.
  
  Which gives us the equation x/30 + x/40 = 8
  To solve, we find that the LCM (lowest common denominator) is equal to the product of the 2 denominators (30 and 40) and it is 120
  
  30 goes into 120 a total of 4 times so we multiply x by 4 on the left side.
  40 goes into 120 a total of 3 times so we multiply x by 3 on the right side.
  
  So we get (4x + 3x)/120 = 8
  
  if we cross multiply we get 7x = 8 * 120
  
  this gives us x = 960/7
  or x = 137.14 miles.
  
  The farthest distance from home that they can plan to go is 137.14 miles.
• 12 years agoHelpfull: Yes(5) No(1)
• Go through options it will be very easy....Ans is btween 120 and 130
• 9 years agoHelpfull: Yes(0) No(0)