# Solving Distance Problems

He then boarded a bus which moved at the speed of 40 mph and reached his destination. Substituting the value of t in 40(3-t), we get the distance travelled by bus is 40 miles.The entire distance covered was 100 miles and the entire duration of the journey was 3 hours. Alternatively, we can add the time and equate it to 3 hours, which directly gives the distance.But they do tell us, this first sentence right over here, "Umaima traveled uphill to the gift store for 45 minutes at just 8 miles per hour." So we're given a time.

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Starting at home, Umaima traveled uphill to the gift store for 45 minutes at just 8 miles per hour.

She then traveled back home along the same path downhill at a speed of 24 miles per hour.

And what's the time coming back from the gift store?

So we can take this distance, we can take 6 miles, that's the distance to the gift store, 6 miles divided by her speed coming back, which is 24 miles per hour, so divided by 24 miles per hour. We're going to have 6 over 24 is the same thing as 1/4. And then miles divided by miles per hour is the same thing as miles times hours per mile.

Now, we know that the distance to the gift store and the distance back from the gift store is the same. Or you could view it as 3/4 times 8 times 1, is going to be-- well, it's going to be 24 over 4. That's going to be 24 over 4 which is equal to-- did I get it?

So that's why I just said that the total distance is just going to be two times the distance to the gift store. So it's going to take her-- actually, she went there much slower than she came back. So it's going to be 3/4 hours is the time times an average speed of 8 miles per hour. For the first part of the trip, the average speed was 100 mph and for the second part of the trip, the average speed was 110 mph. Assuming the time taken for the first part of the journey to be ‘t’, the time taken for the second half becomes ‘6-t’.From the first equation, d=100t The second equation is 630-d = 110(6-t). A cyclist covers a distance of 15 miles in 2 hours. Solution Speed = Distance/time = 15/2 = 7.5 miles per hour. A car takes 4 hours to cover a distance, if it travels at a speed of 40 mph. Let us assume that its usual speed is ‘s’ and time is ‘t’, then s*t = (1/3)s*(t 30) → t = t/3 10 → t = 15.If a person walks at 4 mph, he covers a certain distance. When we express distance in terms of miles or kilometers, time is expressed in terms of hours and has to be converted into appropriate units of measurement. X and Y are two stations which are 320 miles apart. It's the same as the distance to the gift store. Actually, let me write that in the same green color since I'm writing all the times in green color. We don't know-- in fact we know we're going to have different times in terms of times to the gift store and times coming back. So it would take her longer to get there than it took her to get back. So let's see which of these we can actually-- we already know. So 45 minutes in hours, so it's 45 minutes out of 60 minutes per hour. That's going to be equal to the total distance that she traveled over the total time. Well, the total distance is going to be the distance to the gift store and then the distance back from the gift store, which are the same distances. So it's really you could say two times the distance to the gift store. Well, it's time to gift store plus the time coming back from the gift store.

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