Between two bus stops

Wanda lives between two bus stops at three-eighths of their distance. He started the house today and found that whether he was running to one or the other stop, he would have arrived at the bus stop. The average bus speed is 60 km/h.

What is the average speed of Wanda running today?

Correct result:

v =  15 km/h

Solution:

$$\begin{gathered} s_1={\displaystyle \frac{3}{8}}s \\ {s}_2=s-s_1={\displaystyle \frac{5}{8}}s \\ {v}_a=60\text{ km/h } \\ {s}_1=v\cdot t_1 \\ {s}_2=v\cdot t_2 \\ {s}_3=v_a\cdot t_1 \\ {s}_3+s=v_a\cdot t_2 \\ {v}_a\cdot t_1+s=v_a\cdot t_2 \\ {v}_a\cdot s_1\mathrm{/}v+s=v_a\cdot s_2\mathrm{/}v \\ {v}_a\cdot {\displaystyle \frac{3}{8}}\cdot s\mathrm{/}v+s=v_a\cdot {\displaystyle \frac{5}{8}}\cdot s\mathrm{/}v \\ {v}_a\cdot {\displaystyle \frac{3}{8}}\mathrm{/}v+1=v_a\cdot {\displaystyle \frac{5}{8}}\mathrm{/}v \\ {v}_a\cdot {\displaystyle \frac{3}{8}}+v=v_a\cdot {\displaystyle \frac{5}{8}} \\ v=v_a\cdot {\displaystyle \frac{5}{8}}-v_a\cdot {\displaystyle \frac{3}{8}} \\ v=v_a\cdot ({\displaystyle \frac{5}{8}}-{\displaystyle \frac{3}{8}})=60\cdot ({\displaystyle \frac{5}{8}}-{\displaystyle \frac{3}{8}})=15\text{ km/h} \end{gathered}$$

Try another example

Showing 1 comment:

Matematik

I bow to the author of the solution, it is brilliant :)

9 months ago  Like

Next similar math problems:

• Six years
  In six years Jan will be twice as old as he was six years ago. How old is he?
• Bedrich and Adam
  When Bedrich is as old as Adam today, Adam will be 14 years old. When Adam will be as old as Bedrich, Bedrich was two years old today. How old are Adam and Bedrich today?
• 5 people
  Five people have $122000 each, and one person has $539000. How much should each person (equally) pay?
• Journey to school
  On the way to school I went steady step. In the first half of the journey, I counted every second step, in the second half every third. How many steps I do when I went to school if I counted double step are 250 more than three steps?
• Storm
  So far, a storm has traveled 35 miles in 1/2 hour in direction straight to observer. If it is currently 5:00 p. M. And the storm is 105 miles away from you, at what time will the storm reach you? Explain how you solved the problem.
• Round-trip
  A woman works at a law firm in city A which is about 50 miles from city B. She must go to the law library in city B to get a document. Find how long it takes her to drive​ round-trip if she averages 40 mph.
• Cars 6
  At 9:00 am two cars started from the same town and traveled at a rate of 35 miles per hour and the other car traveled at a rate of 40 miles per hour. After how many hours will the cars be 30 miles apart?
• Greg and Bill
  Greg is 18 years old. He is 6 less than 4 times Bill's age. How old is Bill?
• Pedestrian
  Pedestrian came started at 8h in the morning with speed 4.4 km/h. At half-past eleven cyclist started at 26 km/h same way. How many minutes take cyclist to catch up pedestrian?
• Cenda and Pepa
  Cenda and Pepa went to the event. Cenda started alone. Canda started after him for 20 minutes. How long took Cenda to catch him? Cenda traveling at 15 km/h, and Pepa traveling at 25 km/h.
• Two ships
  Two ships sailed from Venice - a cargo speed of 10 knots and a ferry speed of 18 knots. At what time will the ferry catch up with the cargo ship if it sailed 10 hours later?
• Drive to NJ
  Ed drove to New Jersey at 30mph. He drove back home in 3 hours at 50 mph. How many hours did it take Ed to drive to New Jersey?
• Coach
  Average age of 24 players and a coach of one team is 24 years. The average age of players without a coach is 23 years. How old is the coach?
• Where and when
  The truck left Kremnica at 11:00 h at a speed of 60km/h. At 12:30 h, the passenger car started at an average speed of 80km/h. How many kilometers from Kremnica will the passenger car reach truck, and when?
• Klara
  Klara and Jitka went on a hiking trip at 13 o'clock at speed 5km/h. At 14 o'clock, Tomas ride on the bike at an average speed of 28 km/h. How many hours and at what distance from the beginning of the road Tomáš caught the two girls?
• Cyclist vs boat
  The cyclist wants to ride a short distance by boat, but when he stops at the pier, the boat does not pick up passengers yet and is preparing to leave. The cyclist decides that the boat will catch up at the next stop. The stop is 12km far along the water a
• Average speed
  The truck drove 1/2 of the way on the highway at 80km/h. The other half of the way 20km/h. Calculate the average speed