Algebra 1, Math

Question

The speed of a bicyclist is 10 mph faster than the speed of a walker. If the bicyclist travels 26 miles in the same amount of time that the walker travels 6 miles, find the speed of the bicyclist in mph.

Answer 1

Let the speed of walker be x miles/hour

Speed of bicycle = x+10 miles per hour

Then, using unitary method

Walker can walk x miles in 1 hour

Walker can walk 1 miles in 1/x hours

Walker can walk 6 miles in 6/x hours

Similarly,

Bicycle can cover x+10 miles in 1 hour

Bicycle can cover 1 miles in 1/(x+10) hour

Bicycle can cover 26 miles in 26/(x+10) hour

Since, both the time is equal

6/x = 26/(x+10)

6x+60 = 26x

20x = 60

x = 3

Then, 

Speed of bicycle = x + 10 = 3+!0 = 13 miles per hour

Answer 2

This is a simple distance = speed times the time traveled problem.

d=speed ∗ time 

walker distance traveled is 6 miles 

bicyclist distance traveled is 26 milesw 

let x= rate the walker traveled and x+10 the rate the bicyclist traveled

time the walker traveled is the 6miles ÷ x

time the bicyclist traveled is 26miles ÷(x+10)

equate the two time equations and solve for x

 6miles ÷ x= 26miles ÷(x+10)

cross multiply and solve for x

x=3 which is the speed of the walker

(x+10) is the speed of the bicyclist: 3+10=13

Answer: 13 

 

Answer 3

Let's Set the speed of bicyclist is x mph, the walker must be x-10 since the time both people took are same , so we need think of the expressoon of time for both people, then set them equal,(  time equals distance divide by speed,)

for biciclist time equals 26/x, for the walker the time equals 6/(x-10)

so we will have equation :

26/x=6/(x-10)

cross multiply you got 

26x-260=6x

x=13