Dora drove east at a constant rate of 75 kph. One hour later, Tim started driving on the same road at a constant rate of 90 kph. For how long was Tim driving before he caught up to Dora?

Here is the correct setup:

Name | D (km) | R (kph) | T (hr) |
-----|--------|---------|--------|
Dora | d | 75 | t |
Tim | d | 90 | t - 1 |

The equation is set up as follows:

\[ 75t = 90(t - 1) \]

Solving for \( t \):

\[ 75t = 90t - 90 \]
\[ 75t - 90t = -90 \]
\[ -15t = -90 \]
\[ t = 6 \]

Tim was driving for 6 - 1 = 5 hours before he caught up to Dora.

Ok so let T=time from when Tim starts Distance Tim travels= T 90 Distance Dora travels=T 75 + 75 (<as already started) for him to have caught up His distance must equal hers so: 90T=75T + 75 (now minus 75T) 15T=75 (now divide by 15) T=5 :) So five hourse, hope this helped :)

Answered by Jerboa | 2024-06-10

Answer: 5 hours ;

Answered by ahassan16 | 2024-06-16

Tim was driving for 5 hours before he caught up to Dora, who had been driving for a total of 6 hours. This solution is based on setting up equations for their distances traveled and finding when those distances are equal. The speeds and time differences between the two drivers were essential in solving the problem accurately.
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Answered by Jerboa | 2024-10-02